Serious cyclists .... have all types of bikes.
What's most important is that you find a bike that's comfortable for *you.* If you put the miles on it, then *you're* a serious cyclist. If I were in your place, I would try some shops and see if they would rent you a bike for a week or at least a day or two so you could get a real sense of whether it would be comfortable for longer rides (over and hour), which is what's most important given your medical history. The only other thing would be to make sure it has attachment points for racks, or at least a sturdy basket for your weekend touring.