Some health concerns with taking in one year old cat?

I am getting ready to take in a younger family member's cat. My family member has been irresponsible with the cat from the very beginning. She received him from a friend of hers who's cat had a litter of kittens. She has never been able to give the cat the attention he needs and has asked me to take him in. To my best guess, the cat is a long haired orange tabby and is nearly a year old. My family member has never had the cat into a vet, even though I encouraged her several times to do so, to get him vaccinated at least. Therefore, the cat has never been vaccinated or neutered. He has never been on any proper food, my family member often had the cat eat the same food she gives to her ferret. I was over to see the cat about a month ago and his coat looked a bit greasy to me. I have two spayed female cats already and I am going to take the male cat into the vet to have him cleared medically before I expose them to him. My questions are, what health concerns should I be concerned about with this boy? What would be the best way to go about getting him on an appropriate diet without upsetting his tummy with a drastic change?

Some people do use good cat diets for their ferrets, to be fair (though quality varies hugely). I would keep him on the same diet - crappy or not - until he's settled. If medical concerns are coming first (which I would say is a good call), give him the consistence and comfort of having his normal food. Get him vaccinated and neutered, let him recover, and then I would start adding good food to his current diet. The less you can stress him out right at the beginning with new smells, new sights, new places, and new animals, the better - I would say new food can wait.

And then you can just follow a typical slow and steady transition procedure:

Transitioning Your Cat from Kibble to a New Type of Food (Canned, Raw, or Homemade)

Transitioning Free-Fed Kibble Kitties to Timed Meals

Thanks for taking the little guy in. Sounds like he'll be happier and healthier with you.

Cats and ferrets have basically the same dietary needs, so as long as she's giving her ferret a decent diet I wouldn't worry about that. Although there are some very unsuitable ferret foods on the market :/. But let's hope she got reasonably good advice on ferret feeding. And, yeah, even if it is something awful, try to get enough of his current kibble to do a proper transition so he doesn't get an upset tummy. So many changes at once, so it's best to keep some things stable if you can.

At that age my biggest concern would be whether he's spraying. Hopefully not, or if he is let's hope it'll stop right after neutering. He shouldn't have had too long to make it a habit at least.

And of course the usual preventive care like FeLV and FIV test, de-worming, check (and treat if necessary) for ear mites and fleas, rabies and FVCRP shots, etc. If he's been indoors since she got him, he shoudln't have had too many chances to get exposed to something nasty.