I haven't done it for a while, so hopefully, a kind spirit will chime in if I seem to be misleading you.
Mining on Ropsten is not very competitive. You can mine coins with CPU mining and I think you'll be successful with a free tier instance. Keep in mind that you might not be able to stay within the free tier limits if you run it 24/7.
CPU mining scales with cores/threads. After you sync your node with Ropsten, in
n is the number of cores to devote to mining - probably all of them.
You may get away with as little as 1 or 2 GB of RAM. 4 GB should be plenty. I'm uncertain today's disk requirement but I think 50 GB would be ample.
Hope it helps.