I think you need to go to a good bike shop, or maybe a few bike shops, in some city you can get to even if it takes a weekend trip to do it. Tell them your situation and explain what you want to do, but try to get advice from the "old" (38) guy who runs the shop rather than the 19-year-olds working there. They have NO idea....
You don't mention a budget, and that does have some bearing on what you wind up with. I'm 63, a cyclist for 40 years, but I've been off the bike for about a year because of some eye and balance problems, so getting back into it has me thinking about things I used to take for granted. A recumbent may be good for you--I like the idea, but never have really ridden them enough to feel at home. Something like a Rivendell Atlantis (fairly expensive) with fat tires could work--I have one, and I really like it. A lower-budget version that has many of the same qualities is a Surly Crosscheck or other cyclocross bike. Room for tires at least 35mm wide is a good thing from a stability standpoint and won't slow you down much, and you can always put skinnier tires on if you want to. Older riders sometimes are more comfortable with a different setup than the kids--higher handlebars, lower gearing (I'd recommend a triple chainring), things like that. A racing setup with narrow, high pressure tires, a long reach down to the bars and a stretched-out position may be more efficient, but it beats us old guys to death. If you don't enjoy it, you won't ride. There's a good essay on bike fit and related issues on the Rivendell Web site here: http://www.rivbike.com//. Click where it says READ ABOUT BICYCLES & GEAR and you'll get a selection.