Doomworld is your site, as HeadThump mentioned.
Here is a list of available engine ports:
http://www.doomworld.com/classicdoom/ports/ - might not be up-to-date, though.
I'd say casual players can't go wrong with ZDoom as it runs just about everything. It also has a GL variant. Many people also play with prBoom.
There are also eye-candy engines, some even with 3D models, like jDoom.
For levels, browse their idgames mirror
http://www.doomworld.com/idgames/index.php?dir=levels/ (ratings)
Doomworld more or less regularly posts reviews of newly uploaded maps. However, sometimes they are very biased and unfair, sometimes even outrageously so, and partly lacking screenshots.