After all the mucking around with different Linux's (Linii?) you've done, rebuilding a desktop computer is easy.
Here's a few simple rules:
Choose your processor (cpu) first. Take note of the Socket Number, this decides what type of motherboard you need.
Search for a motherboard with whatever features you think you need with that CPU socket.
Take note of the FSB speed of the motherboard you have chosen. That decides what RAM speed you can have.
And of course you'll need a new power supply (PSU) that has all the new SATA and PCIe plug fittings.
For modern setups you'll need a bare minimum of 450 watts, I recommend 600 watts or more and "Dual Rail" which means there's a second 12 volt transformer in there for extra harddrives and USB's.
Depending on the age of your old setup, you may need a new harddrive and cdrom, they need to have SATA plug fittings, not the old IDE fittings with the big fat grey cable.
I do several of these every year for people, and through personal observations (please don't yell at me) for a stable system that should last many more years I'd recommend:
A quad core (core i5) Haswell processor Socket 1150 (intel processor with graphics card built in to the processor chip)
A Gigabytes socket 1150 motherboard with intel chipset. I've had problems with "H" series and "B" series of chipsets but the more expensive "Z" series have never failed me.
I have to admit I haven't touched an AMD chipset in 15 years and I don't know if this is still valid. AMD used to be faster than intel but had more problems with heat and reliability.
All modern motherboards should be able to handle this - at least 8 gig of ram running at 1600 Mhz
For both RAM and Power supplies, whenever you read any reviews they mostly use Corsair as the bench mark. Why not buy the bench mark? They're not expensive.
In poxy Australian dollars 8 Gig of RAM @ 1600 Mhz Corsair will set you back about $50, a Corsair 600 watt dual rail power suplpy costs around $100.
Decent motherbard and processor will set you back another $300.
If you need to replace your old harddrive and cdrom as well you're looking at a budget of around $600.
Maybe not tomorrow but food for thought.
PC cases have used the same standard sizes for parts for more than 30 years now, everything will fit in your old case unless it's one of those Slim Line or Miniature cases.
The only modern difference is ventillation in the side cover but this is important, there needs to be a vent hole there. The PSU sucks air out of the case and blows it out the back,
there needs to be a hole in the side cover so that air gets drawn across the processor then up into the PSU. It doesn't need to be fancy, cut your own hole and glue a bit of fly wire over it.
I don't know how old your monitor is but with many programs theses days, if your screen resolution is anything less than 1440 X 900 the button down the bottom to click OK will be off screen.
Graphics-wise, intel and nVidea chipsets are so similar that some linuxes get the two confused, either drivers should mostly work on both.
Hope that helps.