Frankly, nearly all the animals I ever had (cats and dogs) were strays. And they have made the best pets.
If you are truly wanting a cat in your home, go for it. Before you take it home, and if it lets you LOL, check it over for any obvious open sores and injuries. If everything looks ok, take it home and straight away give it a flea bath. Then get it check out at the vet and get it shots.
You may want to house it in a room or garage for several days to make sure it's not a scratch-holic and to make sure it doesn't destroy anything in your home while you are at work and such.
If you and the stray have a "relationship" - go for it!
