Should have probably said, I've got chronic sciatica. Would this impact the choices? Riding position, saddle, etc
Nah well out of shape, desk job and bad back limits what I can do. Single speed as in no gears? That'd probably suit me tbf, I've never had a bike with gears. I always rode bmx as a bairn.
By the looks of things you'll want something that sits you upright, and something that doesn't involve stretching towards the handlebars. A hybrid is probably your best bet if you want it for fitness, but you could also consider a more traditional bike (a Dutch style bike for example), maybe with a step through frame to help with reducing amount of awkward movement you need to do to get on /off.