I wouldn’t expect much behavior-wise immediately following the neuter. He will likely be out of it for the first day or so. Boys do tend to bounce back pretty quick, so I wouldn’t expect him to be down for long. After that, expect him to get a bad case of the crazies. He will be a little insane as his hormones begin to fluctuate. Don’t worry, it doesn’t last forever! Once his hormones level out, he will start settling into his normal post-neuter behavior.
The neuter should be outpatient, unless the unlikely event of there being a problem. He should come home the same day. You’ll want to bring food with to the vet so he can be offered food before and after the surgery. Once home, it’s a good idea to have some of his favorite foods on hand just in case he needs some persuading to eat. Don’t worry too much if he doesn’t want to eat a lot right away though. Most of the time they don’t need a cone. Most vets only use them as a last resort if bunny won’t leave the area alone. Otherwise, there isn’t much to do. You’ll want to limit his jumping the first few days and you’ll want to check the incisions regularly to make sure there isn’t any sign of infection. Keep his litter box clean, that will help.
Some vets will send home pain meds, some won’t. Some give them a long lasting injection at the vet. Some boys don’t really need them, but it is a good idea to have them on hand just in case.