Here's how I'm been running through the game VERY easily...
Stats:
Str = 1 or 2
Per = 7
End = 1
Char = 8
Int = 10
Agil = 7
Lck = 5
Tag skills were Sneak, Lockpick, and Speech. Pretty much close to how I started my chars in the other fallouts. I raised speech as fast as possible. With 20 skill points from 10 int, it's very nice to raise skills. I found anything over 60 points in speech is worthless. You can wear a pre-war clothes for bonuses, such as a speech bonus. You can also get the bobble head. With 70 skill a 5 luck you'll always succeed on any speech attempt in the game I've found. But having speech that high allows you to do things you wouldn't otherwise be able to and get extra exps in the process and possibly gear. Sneak is just so damn USEFUL in this game though. It affects your ability to pickpocket, stealth crits, and just staying out of trouble. Get this to at least 60+ ASAP.
Lockpick and science are needed in this game for a variety of locks and computers to hack. However, the skill only allows you to attempt, it doesn't help in anyway after that. Computers and Lock skills levels are as follows.
Very Easy = 25 skill required
Average = 50 skill required
Hard = 75 skill required
Very Hard = 100 skill required
If you have 50 skill points and come up to a Hard lock or computer, you can't even attempt it. But if you have 100 skill and come up to a easy lock or computer you still have to do the sequence of hacking or picking. The added skill points don't affect the outcome in anyway, just your ability to figure out where to jimmy the lock or guess the correct password. There are items out there to increase your skill, including a one time +10 bonus from a bobble head to all skills.
So far, I've been unimpressed with any gun out there beyond the 10mm pistol and hunting rifle. Level 16 already and I am STILL using these guns as my main staple weapons. Everything else just wastes too much ammunition needlessly. Ammo is a premium in this game so spray weapons aren't that great. Now I do use the Rock-it Launcher I made, because you can fire just about any piece of junk as ammo you come across. The problem is, that junk takes up weight, and regular ammo doesn't. Then again, after you fire off the junk from the rock-it launcher, you can go pick it back up or just find another piece of junk so ammo isn't a problem with that gun.
Only reason I haven't really messed with other weapons, like say a laser rifle or plasma rifle, is while they do decent damage, their upkeep is retarded! To fix my hunting rifle from low condition to about 3/4's from a merchant runs about 40 caps. To do that with a laser rifle is about 800 caps.
The only other weapon skill I've found useful is explosives. DAMN that skill is actually USEFUL!!!! If you've played fallout 1 and 2 that was one of the worst skills to use. In this game you need it. Nades are all over the place. They do GOOD damage. Mines are great, especially the bottlecap mines. The higher your skill, the more damage your explosives do. On top of that, the skill allows you to disarm traps and collect the traps as more mines, or nades. Holy crap and definite must have skill. I've found a few traps requiring 60 skill, so getting to around there is needed.
From my playing perspective, here's my break down on skills.
Bartering = great skill, but not exactly needed at the beginning. Very useful later one when you want to make those really big purchases like upgrades to your "house" in the game. 60 points is also required for the Master Trader skill perk which grants a 25% discount at all merchants. This is a decent perk! Considering how rare money is in this game.
Big guns = Meh. Missles and the Fat boy are cool, but they shoot SO SLOW and are one shot then reload. If you don't kill your target on the first hit, you are swapping to another weapon. The other problem is the damage on those two aren't usually enough to kill the bigger guys unless you get a lucky crit with one hit, or unless you fire a molerat. The other big guns you can use with this aren't useful either because they will go through ammo like crazy!!!! With ammo so rare in this game, it's very situational when you use these guns.
Energy weapons = Great weapons, just their ammo costs a ton, and the repair costs are crazy, and then they are just rare to find in the game. This means, even if you have a decent repair skill, you will have a hard time finding more of your favorite weapon to keep it fixed up. Also, the damage isn't that much better except on certain enemies than conventional weapons.
Explosives = Great skill. Must have 30 points in it to even get your house in Megaton. Landmines and Grenades are surprisingly plentiful if you use them only for encounters with bigger baddies or LARGE groups you can't pick out single targets from. They do great damage, are cheaper than missiles for about the same damage, and don't require a reload. Now, they don't go that far when thrown, so a good sneak skill is needed to make the best use of them. But the fact is, they "bounce" so you can do some tricky things like bouncing a grenade around a corner and killing targets while still staying hidden. Add to the fact that there are plenty of traps in this game to disarm and you'll appreciate points in this skill even more.
Lockpick = Great skill. But be aware that if you go picking every lock you see, you'll get tons of exps and items, but a lot of evil karma as well. On top of that, this skill is only useful at "tiers" of points. 25, 50, 75, and 100. Any points in between are wasted. With a bobble head and + skill items, any points over 85 is wasted.
Medical = I'm not too sure about this skill. Personally for me, it's a rather useless skill. So far with my playstyle and in 16 levels, I've never been hit yet. Even if I did, I got so many stimpacks and purified waters for health, I just don't see the use for this skill. Now, there have been some situational skills, such as fixing up random people, like Timebomb in Big Town, but beyond that I've not seen much of a use for this skill unlike previous games. There are a couple perks associated with this skill, such as the cyborg perk, which is a decent perk and requires 60 medical. A bobble head and clothes will add +15 skill. Timebomb and others didn't take much skill to fix up, only 40 points. Maybe if I was playing a melee character this skill would be much more valuable but as a sniping character, it isn't.
Melee Weapons = Playing a sniping gunner so this skill is worthless to me. Maybe my next run through the game I'll try melee. I'll say this, there isn't that many great melee weapons out there. The best I've found so far is the Shishkabab.
Repair = Decent skill. Useful for a few quests, like fixing the water pipes in Megaton. The really major reason to have this skill high is to maintain your own equipment without using merchants. Then again, for convential weapons, merchants are cheap. Also, you can only fix an item by "combining" it with another item of the same type. Meaning if you have a hunting rifle you want to fix, you have to have 2 or more hunting rifles in your inventory. What you are doing is scavenging parts from one to fix the other in this game. By using the repair skill you can get your gear well above the merchant abilities to fix gear, provided you have a high skill level. Repair skill also effects home made items you create at a workbench with schematics. The higher your skill, the better the initial condition of the item. This is a skill you can work up to get later. Doesn't need to be maxed out fast, but after you've got all the other skills you want at the level you want them then start on the repair skill.
Science = Same as lockpicking. Read the description for lockpick, but this skill works on computer hacking.
Speech = Staple skill. Without this, certain quests can't be completed or even received. It gives a ton of extra exps and "goodies" such as better rewards for turning in quests. A must have skill to get high as soon as possible.
Sneak = Another staple skill. In Fallout 3, with the game being 3D, it's harder to see what is an enemy all the time. Unless you like enemies constantly sneaking up on YOU, it's better to get the jump on them. Sneaking also affects your ability to pickpocket if you don't mind the negative karma. You can use a stealthboy for a limited time frame, which makes you like the Predator as it bends light around your character, if you don't want to invest points in this skill. However, stealthboys are rare, and they only last for a limited time. Add to the fact that if you attack from stealth you get an automatic critical hit on the first attack to hit, this is a great skill. I suggest getting the Running Silent perk with this skill.
Small Guns = For me, it's my main attack skill. Majority of the weapons found in this game are either melee or conventional guns. All conventional guns are affected by the Small Guns skill. Your skill level in this affects damage output and accuracy. You'll find the hunting rifle to be your best friend if you are the sneaking sniper. One shot one kill if you are patient enough is feasible on just about any target with the hunting rifle. If you prefer a bit more of a stand up fight, the 10mm submachine gun or heck even the 10mm pistol are great as well. The Subbie does great damage, at the cost of ammo, and the pistol just fires a bit slower.
Unarmed = Haven't used it except to beat on Butch in the intro Vault 101 area. Seems
difficult to go this route, but there are certain perks you can get that might be fun with this skill. The Paralizing Palm perk that stuns opponents when you attack them in VATS mode while unarmed looks great. You can also use "unarmed" weapons such as brass knuckles and the pwoer fist with this skill. Although, technically you are "armed" but the skill refers to your pugilistic ability, not really unarmed.
My play style is all about using sneak + hunting rifle + saving LOTS. By sneaking up to my opponents, I am always assured the first attack. I always save before fighting or even before shooting each and every target. Once I picked out the target I'm going to shoot, I turn on VATS mode and aim for the most vital spot, usually the head, and try to get 1 shot 1 kills. Some baddies you can't, but most you can. If you do a 1 shot 1 kill, even if there are others around, chances are you won't "alert" them to where you are. Meaning you are free to snipe the next guy. Yes, I save and often reload over and over again until I get that 1 shot 1 kill, or maybe 2 shots per kill. Why? Ammo is ridiculous to find in this game. Then again, I never have to worry about getting hit this way.
Another thing I do, is while running around, I'm constantly hitting the VATS key. If any baddie is in range, even if they are hiding behind a rock or some tall grass the VATS ability will lock on and zoom right on them. Even if you couldn't see them, you'll know where they are by doing this. Even if the baddie is behind your character the VATS ability will spin your character around.
Now, my play style is very safe and conservative. I have a very low chance of dying and I haven't had a problem killing anything yet. Even bigger bad guys, like behemoths and brutes, I am able to use a mixture of land mines + nades + snipping to take them down without my target even able to fire a shot off at me. This means I can convert all those valuable medical supplies into cash to purchase things I really need, like ammo. .32 Caliber ammo is like gold to me
Another thing, strength for carrying is nice, but if you don't mind using fast travel, it's not needed if you aren't a melee character. So I'm constantly travelling back and forth between merchants with gear or money I want and the area I'm currently adventuring in. I will tell you that it can be annoying when you are picking up some of that heavy arse armor. combat armor, power armor, metal armor, Talon armor...or any of the really heavy duty armor weighs a LOT. Talking 25+ weight per. Even with a lot of strength, you'll find you are doing fast travel runs to get rid of gear quite often as you progress in the game.