Generally to pick out a third+, you should let your current bunnies pick them out. Most shelters allow speed dating, and some breeders and pet stores will as well. The pet store we got our bunnies from gets all of their animals from breeders, and have the breeders information should something happen soon after you buy the animal, or if a health issue arises that you think might be genetic

The reason you want them to pick out the third is because if you just bring another bun in, it could cause them to split their bond possibly leaving you with 3 single bunnies who dislike one another, or break your current pair to create a new pair and single bun who dislike one another, or they may simpley reject the third bun leaving you with your current pair plus the new solo bun since they dislike one another. When you let them pick out their third together, then you know they are both willing to bond with the bun they pick out

I’ve never bonded a trio but just from what I know about bonding i’ll offer this advice-

I’m assuming you already know how to bond since your current two are bonded. as for adding the third I would say bring him/her home and give them some time to adjust to a new home. maybe like 24 hours? just make sure they’re comfortable before you introduce them to the other two. As for sex, i don’t know if it matters as long as the new one is desexed as well. Is there a clearly dominant one in your pair? maybe the opposite of that one would be best but that’s just a guess. i wouldn’t think size is a problem once they are bonded. the only concern would be during bonding if a fight breaks out the smaller one would be more vulnerable.

Hopefully someone with trio experience will see this- but if i were you my top priority would be to allow the new bun at least 24 hours in his new home to get comfortable. that way if he gets stressed during the bonding he already knows he has a safe space to retreat to.

another thing- there’s absolutely no fact to this but in my head it makes more sense to introduce the new one to the pair at the same time. I just feel like if you did it one at a time and one of your bonded pair goes back to their cage smelling like another rabbit it could upset their bond. perhaps if the both meet him at the same time they won’t feel as betrayed. Like maybe allow the new bunny to approach their cage (if they’re in one) while they are together. but again, that’s just my hooman brain thinking!

Gina may be able to answer as she’s just bonded one of her current buns (yum, I love currAnt buns) with a bonded pair that arrived together.
But then Pippi (current bun) is a big softy ! He should be a therapy bun for stressed buns !!