Go for it!
The majority of the cats we have adopted have been seniors. Find a reputable rescue and talk to them about their cats. The good places know their cats well and can give you guidance on who will be a good fit. Keep in mind that though they are seniors, they may live to be 20+ years old, and getting the true age of a cat is a crap shoot.
The only issues we have had revolve around getting cats to get along. Since you are only looking for one cat, that shouldn't be an problem.
Find out what litter, and maybe what food the rescue has been using. Older cats can be stuck in their ways.