I would get him neutered when he is ready, as for handling Olly doesn’t like being handled, last night he was almost asleep, he let me check his ears, his teeth and bottom, claws everything and I tried to pick him up, (He is neutered) he gave me the look of ‘Don’t you dare!’ and ran back into his cage, bunnies are sweet to us and cuddly, but can be a problem like Bam said, because predators pick them up, not all bunnies see this as us being sweet and kind, we mean nice and kind to our bunnies but some don’t see it that way, maybe your bunny will like you just to stroke him, check his claws and teeth, give him kisses and he might give you kisses, but not like you picking him up, if you try and pick him up and he doesn’t want you to, back away, don’t corner him, let him run about, you can stroke him, let him climb on your lap for a treat, but don’t force handling unless it is an emergency, if you get him neutered he might still be the same, or the same for many months, there is no punishment for bunnies, but wear a jumper or long T-shirt when trying to pick him up, bunnies don’t understand everything, like us, everyone thinks bunnies are sweet animals, they are, but some just simply don’t want to be handled and cuddled and that is that and we have to accept it, you can train your bunny to do things when he is older, like come when called for a treat, train him to go in his cage just by asking him to do so, when picking him up you could put gloves on and make sure you put a hand under his bottom and hold him close to you, if after that he wriggles about, carefully put him back on the ground and let him go about doing what he wants, he is male and maybe territorial and could snap if you go to clean his cage, if he does don’t shout at him, try to stroke him and talk calmly to him about something, at 3 months old he does not understand, he is a baby, even babies can attack us if they don’t understand what is going on, before I forget, try and pick him up from the side, this is so he can see you, if you try when he is facing you, he may attack thinking a big bird has grabbed him, bunnies can only see out of the sides, I know we can get upset if bunny won’t let us pick them up, but we have to accept it and not let it bother us, some cats don’t like being picked up, don’t be surprised that after he is neutered that he still wriggles away, neutering is not so we can pick up bunny, I’m sure he knows you love him, I’m sure there is nothing wrong with your bunny, maybe he was interested in something and when you picked him up he wasn’t happy because he wanted to go to whatever it was he was interested in, please note, I’m only going by experience and no way a specialist.
Good luck.