The majority of modern class C's are on a Ford chassis (E350 or E450) with the V10 gas engine. There's nothing wrong with this chassis; it's pretty durable, reliable, and readily serviced. The legroom and general ergonomics in the front cab are adequate for most people, but not by any means exceptional. The V10 engine itself and the 5 speed Ford transmission are well-proven and well-regarded, albeit rather noisy and high revving under load which some people find unnerving and annoying. (This isn't helped by a relatively large jump between 4th and 5th gear, which means very obvious downshifts on the highway when they occur.)
Other chassis that are seen sometimes are the equivalent Chevy chassis (reportedly nicer ergonomically, particularly for tall persons), the Sprinter and new Ram Promaster for small units, and a few larger chassis models for some huge super-C units (Freightliner, etc.). The Sprinter and Promaster are available with diesel engines, though particularly on the Sprinter it's a comparatively small and low-powered engine.
Realistically, for the broad middle range of class C sizes, you'll probably have a Ford chassis, so there's not all that much to consider there beyond whether it's the 350 or the 450.
I'm not a huge fan of slideouts personally, though I may be in the minority with that opinion. Newer ones seem to generally be reliable, from what I can make out, and differences in specific designs are more important than what sort of technology is used to actuate it. (That is, hydraulic and electric ones can both be reliable or less so, depending on the actual design.) Most but not all new models have one or more slides, from what I can tell.
Depending on what sort of health issues you're facing, you might want to consider some class A's as well. The cab area of most class A's is easier to get around in; certainly that's true for pushers since they don't have a big engine hump to deal with. Many class C's also have a step up from the cab to the house, and perhaps another in the middle of the house area, while class A's have a flat floor from front to back.
