Are Stray Cats A Good Idea?

I agree on the vet check. Do it BEFORE you even take the cat to your house. Fleas, mange, ringworm, coxidia, giardia can all be shared with you other pets, and even you. Keep it separate from your other pets for a while so they can get used to the smell of another pet in the house (especially the dog). And double-check the sex of the cat. If it's "chubby" and very friendly, it might be pregnant and looking for a safe place to have it's kittens. If that's the case, be sure to give it a quiet place away from the dog where it can feel that the kittens are safe.