I think the AMD64 3500+ will be alot faster than the Intel P4 3.4GHz, in almost all applications (i'll probably get killed for this lol). I would personally definetly go with the AMD as it's also a great overclocker.
1GB of RAM is usually a good step, as it will nix your page file (not entirely i don't think) and allow for faster load times in alot of apps and overall better performance. 512MB is fine but it's easy to overload with todays games and especially if you are using demanding programs like photo editing or video imaging.
For cases, lianli's are REALLY nice...but for under $100 maybe out of your reach. Enermax makes pretty good ones, Antec/Cheming makes the Alienware looking ones (older style), there's really a whole plethora of cases to look at. You will probably want a thicker aluminum/steel material, full/mid ATX, room enough for at least 4 case fans (unless you are using another method of cooling), and a window if u plan on lights of something fancy inside to look at.