If you use your PC for standard activities like: surfing the Internet, running Office programs, editing a few photos from time to time, listening to music & similar, Win7 32-bit will be just fine as you won't need more RAM to begin with - now or in the near future.
I would recommend running the Win7 Upgrade Advisor click here, OR check your software & hardware individually for compatibility at the MS Compatibility Centre click here.
There aren't any Vista/Win7 related drivers to download for your motherboard at Asus click here or nVidia (click here - choose Legacy > nForce 3 series....). But if it works fine with Vista, it may be OK with Win7, but no guarantees.
What you will also want to think about is which type to buy in terms of Retail or OEM. The Retail version can be transferred from one system (PC or laptop) to another any amount of times as long as it's installed & activated on only one system at any given time. OEM, on the the hand, can normally only be installed & activated on the 1st PC (or motherboard) only. In other words, it cannot be transferred from one system (or motherboard) to another & the licence is permanently attached to the original system (or motherboard). If you dump the system (or motherboard), the licence 'dies' with it. If you opt for the Retail version, you may want to go for the 64-bit version with the future in mind.
Differences between the Win7 Editions (Home Premium, Pro, etc) click here.
If you're a student/teacher, you can get a heavily discounted upgrade version: click here. Eligibility FAQs at click here.
If you need to upgrade 3 systems, consider the economical 'Family Pack' which is only £108 at Amazon click here. That's only £36 per licence/system.
Couple of past threads about Win7 64-bit compatibility with various software click here & click here. I have also personally found just about every 32-bit program works with 64-bit Windows. Some older hardware may be a problem though. Again, you can check your software/hardware at the Compatibility Centre. G