Yes, you should be able to run ultimate on that thing, and in my opinion 2 GB is enough (although more is always better). There are some programs on the net that do not support 64-bit, but most of them do... I've 64, no complications...
As for your graphics card, it depends on the budget, but I'd go for something like this one:
Newegg.com - ZOTAC ZT-86TES2P-FSR GeForce 8600 GT 512MB 128-bit GDDR3 PCI Express x16 HDCP Ready SLI Supported Video Card - Desktop Graphics / Video Cards
or if you have a little more to spend:
Newegg.com - EVGA 512-P3-N801-AR GeForce 8800 GT 512MB 256-bit GDDR3 PCI Express 2.0 x16 HDCP Ready SLI Supported Video Card - Desktop Graphics / Video Cards
Amplid