I found this website with 3 top picks:
http://www.consumersearch.com/steam-cleaners

Either of the first two would probably work for you. The problem with a hand-held unit is that you are holding the water, and water is heavy. With a canister type unit, you can just pull the water around on the floor. With a canister unit, though, you want to make sure the hose is long enough for you to reach where you want to go.

I'm thinking in your situation that a canister unit makes more sense. Hoses are not long enough to reach to the ceiling, but you could probably rig up a little rolling cart to elevate the canister. It would probably work well as a two-person system with one wielding the steam cleaner and the second coming along behind wiping up with cloths. When using my steam cleaner in the bathroom, I always have a large stack of cloths handy to wipe up the steam.

I can't imagine using it on a ceiling, but maybe you could get it to work for that.

Edit: I should add that, when Googling for more info, search for "dry vapor steam cleaner" so you don't get the steam carpet cleaners (which are an entirely different animal). The better the unit, the hotter the steam, the dryer the steam, and the more pressurized the steam -- which means faster, easier cleaning. The units above are all the lower-end units which will produce steam under less pressure and perhaps with more water in the vapor; this means they clean more slowly. However, they can still do a great job!

I have the Bissell Plus and love it. Even my 7 yr old Granddaughter asks to use it on the kitchen floor. Can't turn down that offer! Works great on wood, tile and linoleum. It also has an attachment for carpeting but the directions say it is not a cleaner, just a carpet refresher. I did get some wax on my carpet that I've been struggling with for a couple of years and it has really helped get that up.

After I killed off a Shark, and a little hand steamer, broke down and bought a Vapor Storm. Have been using it the last two months rehabbing a rent house that was not cleaned for 5 years. Steamer and putty knife found the tub under layers of soap scum. Still have to tackle the tile shower stall and its glass (think it's under there) door. Great for the ickies in the refrigerator gasket, oven vents, etc. Floor attachment cleaned the dreaded under the frig patch with nothing but the steam and microfiber pad.

How did you manage to get wax out of your carpet? I have a Shark floor steam cleaner and I hadn't even thought to try that.