Hi and congratulations on your new bun!
It can be really scary when you read up on rabbits, but it does get better with time. There are a few dos and don’ts – rule nr one is keep an eye on appetite and poop. If a bunny doesn’t eat or poop in 8-12 hours, contact a vet. Try to get your bunny to eat grass hay and let him have access to unlimited hay and water 24/7. That’s the basics of the basics.
Bunnies tend to molt a lot, and as you are saying, you want to prevent them from ingesting too much hair. If you pull loose tufts out, it’s doubtful if you bun will bite you. It won’t hurt him when you pull out tufts that have already come loose. If there are mats, you should cut them off instead of trying to comb them out, but don’t cut too close to the skin. He might not look pretty after you’ve cut out mats, but the hair will grow back and he’ll be pretty again.
Brushing is rather a must with a shedding bunny, but if he gets really scared, try to pick out hair instead of brushing. When you’re done, wet your hands and run them through his fur so you catch as much loose hair as you can. If he has short hair you can even lint-roll him with a generic lint-roller (name brands have too high quality glue to be suitable for use on a bunny). Lint-rolling has the added advantage of catching the hair so it doesn’t fly around the room.
Hay-eating is good for the tummy and will help him get the hair he inevitably will ingest through his system without causing a blockage. If you’ve started him on fresh greens, you can serve them dripping wet so he gets water in him, that helps the tummy too.