I own a Playstation 3 and am quite satisfied with it. I have been strictly a console gamer since I was a kid so maybe my opinion is a bit objectified but it's worth buying in my honest opinion. Right now I own a 32'' LCD TV and was looking for a high-definition format anyway because standard DVD's don't look the best on LCD, so it was either Blu-Ray or HD-DVD. Already owning an XBox 360, I decided against getting the add-on and splurged getting the PS3 - couldn't be happier.
Games look outstanding in 720p and the online service is steadily improving. I love to play games online and that's why I was hesitant at first because nothing can stack up against Xbox Live but I've been pleasantly surprised. A lot of my free time lately has gone towards playing Resistance: Fall of Man online - that game is just addicting. So far I have nothing to complain about really. The graphics are awesome, games are top notch and the online service is seeing some great improvements especially with the frequently updated Playstation Store. I don't want to bore you with specifics, but if you want some more pros/cons or have any questions, feel free.
As for gaming on it with a CRT... no idea but if you only have a CRT I'd advise you get an HDTV set first, before a PS3.