It don't matter, a PC and a Bitcoin miner is completely different.
You can't use an ASIC miner to increase a PC's performance and vice versa.
A Bitcoin miner would not reside within your PC, for most part anyways.
You can invest in graphics cards but those aren't really feasible for mining unless you get an army of them.
However, the graphics card retains a better value and can be used for gaming and video rendering but also get obsolete quite quickly.
An ASIC miner has one job, perform cryptology services, nothing else... well that and make heat is a valid argument for Canadians
Essentially, when you mine Bitcoin via ASIC, the device alone does the all work, neither a PC is involved or not.
The PC component (Control Board) is usually built in the miner... well, the good builders do.
However if you mine via GPU then having a computer as controller is always a good idea since GPU's don't have a built in mining software.
In other words, you only need a PC in ASIC mining to set up your pools and change IP / DCHP.
You could even ask the builder to preset your pools and then you don't even need a PC.
Other than that, most modern ASIC miners are rather hands free.
My recommendation, start with an AntMiner S3 ($250 - 440GH/s), don't bother with GPU mining.
If you want to spend less, try the U3, which is a USB miner which I beleive is under $100
Best of luck to you and welcome to the game
32MB of RAM.) or to my better and new PC?
What Operating System are you running with 32MB of RAM?
I cannot for the life of me imagine a motherboard that can adapt for such small amount of ram... myThinkPad has 32GB RAM lol