In the herd here, it's mostly been the bucks who have been the in-your-face friendly bunnies. The buns here get handled almost literally from the moment they're born, because of the coat maintenance they will need as adults. But they're not a good pet because they're angoras. Although perhaps a pet Swiffer may be handy to have in the house except you'd then have to clean the rabbit instead of the floors. Another bunny breeder here in town handles hers from birth since they're bred to be pet bunnies. She's got the Netherland Dwarfs and Holland Lops although she only has one or two females of each breed so she has time to hold all the babies. But, we're in Hawaii, shipping to the mainland would be absurdly expensive when you've got options already over there.
You can train a bunny to quite some extent. It's best to get one with a fairly calm temperament to begin with and then bribe them into good behavior but if all you can find is a skittery bunny, start from there. When they learn that if they go near you a tasty leaf or some other bribe will appear pretty soon they will be around you all the time.
As for nail trimming, we put the bunny on the grooming table (a bit of carpet on a table will make any table into a grooming table), then lift the chest while scooping under the tail end. Kinda tuck them into the crook of your arm. They'll be upside down and wiggling, wait a few seconds until they quit wiggling and then trim toenails. Turn rightside up and administer ear rubs and a ti leaf. It's not gonna be their favorite activity, but they will get to tolerate it fairly well.
But, we've been breeding for temperament for generations so maybe our experience is all skewed.