Honestly, you can probably get a great server from ebay or craigslist for less than replacing the power supply. I know HP Proliant servers best, so briefly:
DL servers are rack-mount; ML are towers.
Like BMW, they have 100, 300, 500, and 700 series (Yes, I know BMW doesn't have a 100 series, but roll with it.)
At the end of that will be a "G" number. This is the "generation" of the server. G2's are the second generation; G6's are the sixth generation. I'd recommend at least a G4. G6's and G7's are brand new, but price will reflect.
I'd recommend against anything 100-series. I have the most experience with the DL380, DL580 and DL760. The 760 will probably be waaaay more machine (and less disk) than you need. Different configurations of the 300 and 500 series will store different kinds of disk. G4s will be either Ultra-320 disks or SAS, but G5's and later will usually be SAS. Ultra-320 disks are widely available cheaply; it is aging tech, but I still would buy them for personal or small business use.
Just be sure to get the dual power supplies, and read up on using iLO (Integrated Lights-Out - it's a built in VNC server and virtual power button, among other things.) It's fantastic and will change your life.