I have made plenty of working backups on my G4 tower with no problems yet aside from stuff I caused myself. You will need Toast.
Insert disk, select copy and go from the drive. Click the big red button select 1x/2x (whatever your preference), click Record, and it will make the image and then spit out the game and ask for the DVD-R. Drop it in in the drive and let it go. When the game is done it will DING (like a Toaster ) and then you can let it verify or eject it. I don't verify and all my games come out fine. All the same rules apply about media and such.
What I would like to know is about patching and a Mac. I am not sure how the patches work, but if they are any kind of .exe file then Apple users are SOL.
The mini is a great little machine, but keep in mind that the expansion capabilities are nil. You can add RAM and thats about it. Bigger HD, better burner, all that stuff is not really option, but considering they start at about $500, you can always just buy a newer better one for about the price of those things together.
Don't buy Apple RAM. It is no different from PC ram and is highly overpriced. Upgrade the other things that are not accessible like the optical drive and the hard drive, but then hit best buy or an reputable online store and get the RAM for cheaper. No matter how hard it is to change other things, apple has always made the RAM accessible for expansion.