Modern PCs are plenty faster enough for general purpose use, so you will get far better value with a premium branded desktop. Its only worth doing self build if you need something unique... ...and most people aren't really up to the job of dealing with the thermal requirements (partly because 99.999% of generic cases are not up to the job).
The 2 PCs I use at home as general purpose desktops, one is a Dell Dimension 9200, Core2 quad with 2Gb RAM, 965 integrated graphics and 240Gb Crucial m4 SSD, circa summer 2007 (so over 7 years old) and cost around £450 at the time, the other is a HP 6720s Core2, 965 integrated graphics, 2Gb ans 120Gb Crucial m4 SSD, circa Nov/Dec 2007 (so 7 years old) and cost around £350. They are both plenty fast enough, so as much as I quite fancy the idea of a nice new shiny one, its difficult to justify. I'd also hazard a guess that both are faster than anything I could buy for under £500
Absolutely no point in trying to use "old bits lying around", as these will cripple performance of a newer system. Trying to save money in this way is false economy IMHO.
If I was looking to replace one of mine, and run 32bit Windows 7 on one (not worth using 64bit Win7 unless you really do have to access lots of RAM), for general purpose use I'd be looking at 4th gen Core i3 (i5 and i7 not really worth the extra for general use), 2 - 4 Gb RAM (32 bit Windows will struggle to see more than about 3-3.5Gb), use the i3's onboard video, and tie it together on a Series 7 or later chipset.