Sound like you've got yourself a nice system though since you have a turboboard with 68060 CPU you'll run into a few problems just now in the beginning. But before I go into that what ROM does you have? If what you say is correct (a hand with a blue disk) then you have old 1.3ROM's in the machine not 3.0 or 3.1 as it's designed for.
Ok that said here comes some explanasions I hope can help you some:
Since few games work with the 060 CPU it's safe to say that you'll have your work cut out trying to run a game from floppy. There are however software that will allow to run the games from harddrive so don't worry about that yet.
You'll first have to get hold of a harddrive... Settle for no more than 4Gb just yet (original OS3.0/3.1 won't support more unless you pach it and run a different filesystem and that's another chapter that we're going to jump over for now).
Because you have a 060 CPU you can't even install OS3.0/3.1 from the original OS disks as they lack the 060.library... as a result they will fail. Get a friend to make a copy of the install disk and have him add the extra libs onto it (
060 and 040 dummy libs).
Now the install disk will work and after partisioning and installing the OS you'll still have to manually copy in the extra 060 and 040 dummy libs to LIBS: .