Hi Jack, Welcome to SPCR
In terms of PSUs almost all generic PCs use the "ATX" (physical) size standard which gives the height, width, depth and rear mounting screw positions. Some PSUs are longer (extend deeper in to the case) which can be a problem in short cases with long optical drives. There is also an "sfx" (also sometimes called mATX) standard, the PSUs are a lot smaller and less common/more expensive, I doubt you have/need one. The connectors tend to be backwards compatible, i.e. newer PSUs will plug in to older systems but is not always the case the other way round. The newest systems having 24pin ATX and 4 (or now even 8 ) pin ATX 12V, SATA and PCIe (1,2 or now even 4 of 6pin for GFX card(s)) which older supplies may not have. You can get adaptors in most directions but it's not an ideal solution and you need to look at the capacity of the PSU. In the past the total capacity of the PSU was split fairly evenly across the 3.3V, 5V and 12V rails, modern PC now have the majority of their load on the 12V line and it's taken a while for PSUs, especially cheap ones, to catch up to this fact. Take a look at SPCRs measure of power distribution.
In powering a modern PC it is almost entirely the 12V line that needs to be looked at, especially in this age of high powered graphics cards especially in SLI/crossfire.
All of which is interesting but in your case not relevant as I'm 99.9% certain your CPU is powered off the 5V line as my Asus A7N8X is and the A7V333 lacks the 12V ATX connector. In my case confirmed by monitoring voltages when going from idle to full CPU load, the 5V drops and the 12V rises.
I recently had to get a new PSU and looked at the 2 main favourites round here of Seasonic S12 and Antec NeoHE. From airflow point of view the NeoHE would have been better in my case but it's limited to 70w on the 5V line and my overclocked CPU is probably up around 90w! I went with Seasonic S12 380 (rated 130w on 3.3+5V) and it mostly runs it's 120mm fan at minimum speed around 800rpm, which is pretty damn quiet. As it works fine for me I suspect it would work well for you too, possibly a little louder if you have no rear case fan. There are plenty of other options and we could make more suggestions if you let us know what's available in your area (at what prices) and some details of your PC, eg CPU, graphics card, case, fans etc.