Sorry for my ignorance, I am new to all this. Up to now the most I have ever done is install a drive or two.

I hope later in the year to begin my first quiet project from scratch but until then I have an old machine with a Socket 939 Athlon 64 4000+. Quiet it is not. I have ascertained that much of the noise comes from a rattly HSF so I want to fit something a bit more SPCR like. Will mounting kits for current AMDs also fit mine, or do I need to look for something particular?

Well 99% current coolers which attach on retention bracket will go in older 939 and 754 sockets. When coolers are installed bolt-thru then compatibility is not quaranteed.

Look at the reviews and specs on the heatsinks you're looking at, and they will usually tell you compatibility if the manufacturers webpage won't.

Some HSF are specifically made for LGA775 sockets (like some of the Arctic Cooling lineup), but most of the major players (Scythe, Thermalright, Xigmatek, Noctua) should be compatible with the 939 socket.

I found a compatibility chart. It seems nearly all heat sinks are compatible either out the box or with a mounting kit (e.g. Thermalright). Unfortunately the recently reviewed Noctua NH-C12P is one of the few which is not. A shame because I think it would have fitted in nicely. I am not sure I have the space for a big tower like the HR-01 Plus so it may have to be a Mini Ninja.

The Thermalrights will most likely fit with Socket 939 for newer line. Also Xigmateks coolers are very likely to be compatible, since they use retention bracket.