I like the A600 due to its small size and if you simply want to play games on it, there is hardly any need for an A1200. Since your floppies aren't working, I'd still recommend that you open it up, add an internal (CF) HDD as well as Kipper2k's 4MB expansion. With just 1MB RAM you're not going to be able to play many games from the HDD, and you would need floppies for everything (which you don't have). With 4MB extra you should be able to run most 1, 2 or 3 disk games through WHDLoad from the HDD and still have the PCMCIA slot available for file transfers between the PC and the internal HDD.
Regarding your floppy troubles, I just cleaned out my Amiga floppy collection, and after doing XCopy format with verify (on all non-originals) I threw out about 50% of them. The rest still seem to work fine with no bad sectors or weird noises. All my original workbench disks still work fine. But this also depends a lot on where they have been stored. If all your disks have been stored in a moist cellar or attic, I'm sure they degrade a lot faster.