I've used many of the Dell OptiPlex GX620 -- an 8 year old / 2005 machine -- with Windows 7 64-bit:
- Pentium-4, 64-bit, 3.4 ghz, single-core
- 2 gig DDR2-533
- Network works using Microsoft's generic driver
- Sound works using Microsoft's generic driver
- Video is not supported, so its the "Standard Graphics" driver.
For your project, this will be very slow and you will spend much time waiting for it. You will likely not enjoy this experience.
If you don't have enough memory installed, Windows will use virtual memory on your hard drive, and the more virtual memory is used the slower everything gets.
P4 equals "Core 1" performance. Modern "Core 2" are effectively double or more in performance for the same ghz as an old P4. Compared to a modern "Core 2" CPU with multiple cores for you it will be like running at 1.4 to 0.8 ghz.
Assuming you will use the cheapest Windows 7 OEM Home edition, that's about $100.
You need more memory and are probably will need about $30 there.
If your computer does not have a supported video chipset, then you will be stuck with Microsoft's generic and slow "Standard Graphics Adapter" driver. This will work, but no hardware acceleration so performance will be even worse yet.
You could plug in a graphics card with Windows 7 support, but if your goal is to save money, this is not a very good way to go.
I would suggest looking for a computer recycler or local computer refurbisher that sells older machines with Windows 7 already installed. You will likely get a much better performance machine for $250 or less without the hassles of trying to make an ancient computer work.