Stray cat keeps coming to my house, should I adopt or send to shelter?

Aww, sounds like the kitten adopted you already. From experience, do a vet check first for health and to confirm age, then decide. If cost is the worry, look for community vet clinics or SPCA which sometimes offer subsidised spay/neuter and vaccination programs. Set a small monthly budget, cats really aren't that costly, mainly food, litter and yearly vaccine. If your family truly cannot keep it, don't just dump at a shelter, try TNR (trap-neuter-return) via local animal welfare groups, or find an adopter through Facebook adoption pages. Feeding it and then abandoning is worse. Since it's already comfortable at your porch, giving it a home is the easiest happy ending.

From my experience taking in strays, the first step is a vet visit. Get it checked for fleas, worms, and basic health, plus a deworming and first vaccination. Kittens can carry things but most are treatable and it's not that expensive for a basic check. If it's healthy and your family is warming up, honestly adopting a cat that already chose your porch is one of the best decisions, they're low maintenance compared to dogs. Also please spay or neuter once it's old enough, that prevents a whole colony appearing later. Shelters here are often overcrowded, so if you can keep it, that's kinder. Start with the vet, then decide with a clear picture.