This topic has been covered before in itsallPC, however, I'll summarise.
Obviously a 64-bit CPU is required to run 64-bit Windows.
- Pentium 4 600-series and later (includes Pentium 4 Extreme Edition 3.73 GHz)
- Athlon 64 family (including FX, X2)
- Core 2 Duo
- Celeron 3x1, 3x6, 347, 352 and greater
- Pentium D family (includes Pentium Extreme Edition)
- Pentium E2000-series
- Manila core Semprons. There's no model number pattern to identify them. Use cpu-z or simillar
Specific points of 64-bit Windows (mostly also true of Windows XP Professional x64)
- 64-bit Windows can address a lot more RAM. 32-bit supports a maximum of 4GB; 64-bit supports a maximum of 16GB. This is of course, useless to you at this point.
- 64-bit Windows can execute 64-bit operations in hardware. Software specifically written with 64-bit optimisations will be significantly faster than 32-bit versions.
- 32-bit software still runs on 64-bit Windows, although there are many reported compatibilities issues
- 16-bit software does not run on 64-bit Windows
- 32-bit drivers cannot be used on 64-bit Windows. Most major manufacturers now have stable 64-bit drivers. I believe there are still only flakey or non-existent 64-bit printer drivers though.
- 32-bit and 64-bit Windows Vista are identical in features and aesthetics (This is not true of Windows XP Professional x64)
If you plan to upgrade your OS again in a few years, go with 32-bit. If you can put up with a incompatibility issues for a year or two, go with 64-bit.