If you want a copy of Linux Mint, you can order it from one of the vendors listed in the main website. As far as I know, Mint does not ship free CDs as Ubuntu does. If you want a Mint CD quicker, you can download and burn your own. I can suggest the torrent as a good option since I have never gotten a bad download that way. I do not know what your hardware/software combination is on your end, so you will have to get the downloading and burning done on your own, or with the help of another Windows user.
The best way to see if Mint will run on your hardware is to load the Live CD. It is very similar to Ubuntu, so you may or may not have the same issues you had with Ubuntu. You also might wish to consider matching the ISO to your hardware. If you have 32-bit, choose the 32-bit version. If you have 64-bit, consider using the 64-bit version.
Once you get something up and running, you can post back for any answers to questions you may have. Good luck.