why do you want to use something as outdated as a P4? If you want to go cheap then you can't get cheaper than an Athlon II X2.
The cheapest Athlon II X2 with the cheapest/basic AM3 motherboard will probably be a hundred bucks (and with onboard video too). Yes you'll need DDR3 RAM but it'll cost you so much more to get older memory tech as manufacture is winding down.
2GB DDR3 kits of basic RAM are cheap anyway.
From there it all depends on what else you want to put into the system.
My point is if you have an old system you can recycle into a server then yes stick with what you have laying around, but if you're going to actually spend actual money then there's just no point in getting such ancient tech as a P4 - you'll just end up paying more for it than today's modern budget components.