See if they can rent or borrow a couple of different styles of commuter and cruiser styles to try them out. Test rides are good, but often too short to really tell you much. Honestly, a hybrid with some fairly fat tires would probably serve them well, but everyone has their own preferences. You can get cruisers with internally geared hubs that give them a range of "speeds" with simple one-handed shifting.
Not just no but Oh Hell No on the adult tricycle (not talking three-wheel recumbents here). Unless they have some kind of disability, there is no reason that a 65-year-old can't ride a two-wheeled bicycle of some sort. I know dozens of people in their 60s and older riding regular bicycles up to and including hard core road bikes, though townies, cruisers, commuters and hybrids do seem to be the popular choices.
BTW, ILTB, who you calling "elderly". Now get off my lawn
Just one example of his n hers cruisers
and a typical hybrid