HP Pavilion Slimline s3700f: Athlon 64 X2 5000+ 2.6 GHz dual core processor.
Chipset type: NVIDIA GeForce 6150 SE/nForce 430.
Video Memory 128 MB
Expansion Slots Total (Free) 1 ( 0 ) x Processor , 1 ( 0 ) x PCI ,
1 ( 1 ) x PCI Express x16 , 2 ( 0 ) x Memory - DIMM 240-pin
Graphic cards will be measured in Mb's not 32 bit or 64 bit. The terms 32-bit and 64-bit refer to the way a computer's processor (also called a CPU), handles information.
32-bit and 64-bit Windows: frequently asked questions
Based on the above specs. Of your desktop, I would suggest that you look for a PCIex16 graphics card. Of course it needs to be sff (small form factor) or there are conversion kits available that convert standard graphic cards to small form factor:
XFX MA-BK01-LP1K Low Profile Double/Single Bracket Kit at TigerDirect.com
PCI express 2.0 x 16 graphics cards will also work with PCI express x 16 however, it will be bottlenecked to the 1.0x specification.
Hope this helps.