OP's not going to get USB3 out of an '08 iMac.
I think I'd be mildly inclined to replace this machine rather than upgrade it. It wouldn't be all that hard to change out the hard disk for a newer / larger capacity one, and it wouldn't cost all that much. I don't know how hard a job it is, if it's anything like the early '09's it's tedious and fiddly but not intrinsically difficult. However once you do that you're still limited to a max of I think 6 Gb ram, and El Cap (supposedly Sierra will run with some fooling around).
If you just need a few more months, the hard disk upgrade is definitely an option. Or, an outboard USB disk to relieve the immediate storage problem, but it will be slow since you're limited to USB 2.
You might look for a refurb or gently used "late 2015" iMac, which will be a significant improvement over your current machine and ought to be cheaper than brand new.