Amazing how many people don't read the op's post with any degree of comprehension. Guy's, he said he is on a tight budget, this rules out most of what has been offered as a solution.
The best carbine solution for the money is the Hi-Point in 9mm. Put a red dot on it and a couple of extra mags and you are good to go for under $300. I own one along with an AR and a Kel-Tec Sub2000 and an M-1 carbine, and several AKs, and etc. My recoil sensitive GF only likes the M-1 and the Hi-Point out of this bunch, and the M-1 is twice the money and the ammo is harder to get.
The main drawbacks to the Hi-Point are availability, there's a lot of demand, and magazine capacity, factory mags only hold 10. You can get 15 round magazines made by an after market supplier I won't name, but they are only useful for holding down your spare targets at the range. Oh, there's one more drawback, they are truly ugly. Mine has been as reliable as I could want and accurate to boot. Evan people who hate the pistols usually have good things to say about the carbine, and of course they have a lifetime, no questions guarantee.
I've read that 9mm picks up about 2 to 300 fps from the longer barrel, but I haven't tested it.
In your price range and health situation I think that this is your best bet. Do a search on Hi-Point 995 carbine and you'll find lots of info.