would that cause Windows 8.1 to make any changes to things like the registry or anything else?
Yes, but that should not cause any problems.
Please elaborate.. what should I look for?
Most motherboard makers maintain QVLs (qualified vendors lists) of compatible RAM and CPUs for each of their boards. There are too many RAM makers and models for board makers to test them all so you don't have to buy listed RAM, but you do need to buy RAM with the same specs as listed RAM.
But for CPUs, because motherboards either support AMD or Intel, and because the socket and chipset only support a limited family of CPUs, board makers can verify and list the supported CPUs. So you must buy a listed CPU to ensure compatibility. Your board's CPU QVL is located
here.
That said, typically when upgrading a system, especially older systems like yours, the CPU comes after RAM and graphics (depending on where you are starting from). Adding RAM generally provides the most bang for your money. If you have less than 4Gb of RAM, I would add RAM first - especially if you have integrated graphics as that steals... err... shares a chunk of your precious system RAM for graphics processing.
Unfortunately, it looks like your board only supports a maximum of 4Gb of RAM. Still if not there, I would bump that up first before buying a new CPU or a new graphics card.
If you have integrated graphics, installing even a fairly basic graphics card can significantly improve overall system performance. Not only will you likely have a nicer GPU on the card, but the graphics card will come populated with its own RAM dedicated for graphics processing. This will allow that previously stolen... err... shared system RAM to be released back to the CPU. So when starting with integrated graphics, adding a card not only provides better graphics processing, but you get a little boost in RAM too. But not only that, with more RAM, you CPU and OS will not have to swap data to and from the page file on the sssllllooowww hard drive near as much - which also increases performance and decreases thrashing (lowering wear and tear) the drive.
Another note; CPUs and larger graphics cards can be pretty power hungry. So you need to verify your PSU can handle the extra demand before installing either. Adding RAM generally does not require a larger PSU.
So my advice, especially since this is an older system, is you need to evaluate your current system specs and see if upping your RAM and/or adding or upgrading your graphics might be a better option than swapping out CPUs.