Check the motherboard, what RAM does it take? If it's DDR2 or older it's worthless and you essentially have a free case.
Otherwise you have a case with a motherboard, because everything else is probably worthless.
Upgrading ancient computers carries few advantages over building from scratch. Often every part needs replacing, and the cases rarely give enough airflow for proper cooling of modern parts. Even if the motherboard does take DDR3, does it take USB3? HDMI? Display port? These are things that are standard on modern motherboards that were far less so two years ago. A motherboard with these features will run you somewhere in the $50-$75 region. That said, it's good to buy a good motherboard because no-one likes replacing them. You have to completely rebuild the pc to replace a motherboard.
Anyway, if the computer is workable for upgrades, here's my order of what I'd do:
1. CPU cooler. Office computers have the worst coolers, a $30 coolermaster will do the trick. Better cooling will help you if you want to overclock it, but It'll also stop it from sounding like concord.
2. SSD, with older computers this makes far more of a difference than RAM. If the computers newer or has a stupidly small amount of RAM (less than 4GB) get RAM first.
3. RAM. 8GB minimum, make sure the motherboard can take it before you start doing anything.
4. CPU and GPU. Whatever the motherboard can take. Spend as much on each component, too often people get an i7 and then use the fucking integrated graphics.
Another thing you may want to consider:
Is the power pack good enough? Enough power to run a decent system? For an average system 430 W is the lowest you can really get away with. Make sure it has enough power ports for your hard drives, optical drives, SSDs, etc.
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