It's a tough call.
I only know of recumbent stationary bikes which I do not think are actually better for back issues because they allow you to slump.
When you are cycling you should engage your core muscles and as they increase in strength you will find that you will probably notice a decrease in your back issues.
I would definitely recommend a trike because it also gives you a more similar experience to riding a conventional bicycle, so if as time goes by you need the stability of three wheels less it will be less of an adjustment.
Good luck and happy riding.