It sounds like you just want your server to be a file server for your lan, will you be using it for anything else? Web server, FTP server, backups, db server, etc???
If you want to "learn more linux/unix" then I'd suggest Slackware. It is not the easiest to admin, nor is it the most capable, but it's extremely stable and reliable. Many Unix geeks got started on Slackware boxes in the 90s. The biggest downside to slackware is the package management suite. You can automate a lot of the process, but the package management still can't handle dependencies. Also, there are not a lot of packages, so the likelihood of needing to compile your own binary from source is much higher than with other common distros.
If you already know your way around a unix box, and you want a highly secure server, then you might want to consider OpenBSD. It is known to be the most secure OS "out of the box." You can share files in OpenBSD with Samba the same as with Linux, however, if you want to access windows shares you will need to install "sharity light" to do that. (however, without it, windows and linux clients can still access your files just fine.) The install is a bit tricky, especially the first time around. There are a decent number of packages available, all of which have been audited, and as an added bonus, OpenBSD is able to use the FreeBSD ports tree. This means that there are thousands upon thousands of additional programs that can be very easily installed if desired.
If you want something easy to maintain that's highly stable, and is also not too challenging to install, then I'm gonna recommend Debian. They have lots of packages and their package management software is second to none. Ubuntu is another option, it is generally "easier" to install, and it has more up to date packages, but the cost of "newwer" packages is potential instability. It's up to you if the risk vs reward ratio is attractive.
Personally, my file server runs on Slackware. I have about 3TB of space that I access via samba shares. In addition, I can get at my files outside of my home network via FTP. And I've got daemons running pgsql and apache too. As an added bonus, I have a little ventrilo server up and running for gaming with friends and I used to run eggdrops on it when I was into IRC.
I also have an HTPC running on Knoppix (Knoppmyth technically)
Then I also have OpenBSD running my router/firewall (old celeron box)
My laptops (ones a P4 2.4 and one's a P3 450) both run OpenBSD and Windows dual boots.
I think I like OpenBSD the best overall, but I'm the most comfortable in Slackware...
You can read up on most of the popular distros here:
Distrowatch
Choose whatever you think will like the best. Samba is pretty easy to set up, especially with SWAT, so no matter what distro you choose, you should be able to run what you want.