Over the last 35 years I've almost always had 3 cats, all rescues or strays, 15 in total, 3 were kittens, the rest adults, usually 2-3 years old, a couple a bit older.
All have settled in relatively easily, usually after a few hissing spats with the existing incumbents. I've lost one young cat to a car accident, one 4 year old to a sudden heart attack, the rest have all lived to old age with no major medical problems.
I no longer look for kittens, too much hard work, as said upthread, with a young adult you can get a good idea of the temperament, they're usually streetwise, and they're litter trained. Also many of my cats had spent over a year in the rescues, 'cos nobody wants adult black or black and white cats.
All of my cats have been very different, but adorable in their own ways.
I'd look for a local shelter, RSPCA and Cats Protection can be a bit difficult to deal with, my local shelter TVAW are awesome if you're in the Reading area.
I don't believe that any shelter would deliberately let you take an ill or difficult cat without making sure you knew what you were getting