Do you already have a desktop computer at home? If so then I would suggest just acquiring a new graphics card for it and trying out mining and getting a feel for it before investing in building a whole rig.

IMO it's important to have high quality power supply(s) and components with a warranty since you will be running the equipment non-stop for a while. You may get some life out of a second-hand power supply such as the one already in the system you mentioned purchasing, however it will most likely die on you at some point and then you will have to replace it which will add to the cost of your build. I think it's better to just start with a reasonable warrantied power supply and then at least if it burns you can replace it!

Also, I learned the hard way that if you're serious about keeping your rig going and earning the maximum you must have at least 1 spare power supply around so that if one suddenly pops on you it is immediately serviceable thereby reducing your down time. It sucks big time to lose weeks of mining time because you are waiting for a replacement power supply to come in.