I’ll try to answer your questions in order!

So, we were planning on getting our male teenage rabbit a friend, but it turns out he wasn’t neutered. He’s getting neutered on the 1st of June. How long afterwards should we wait before starting to try and find him a friend?

A good rule of thumb is 3 weeks post-neuter for males. That’s usually enough time for their hormones to stabilize. 🙂

Second, how does that work? Are you able to have your current bunny interact with the new one to see if they’d be a good fit before bringing the new one home? I don’t think I’d be able to handle two bunnies who were constantly attempting to fight, even in the beginning.

Some rescues do “speed dating” where you can bring your bun in to try to find a good match (or at least rule out bad matches). Some shelters also do “foster to adopt” programs for bonding, where you can bring a bun home on a trial basis to see if bonding will work out. Most pairings do work out with time, and almost all require some work to get them there. “love at first sight” bonds are very rare, but about as rare as “hate at first sight” pairings. So even if you can’t do dating or a trial, chances are you’d end up with a workable combo. My first pair was a very difficult bond (partially due to some mistakes I made early on in the process), but I eventually did bond them and they were completely inseparable.

And is it easier to bond a male with another male, or should I try and get him a (spayed obv) sister?

male-male pairs are possible, but on average male-female tends to be a bit easier. This holds up in my personal experience as well when I tried to bond a quad of 2 females and 2 males (all the m-f combos were fine but the boys were just NOT getting along). Especially if you can’t do speed dating, opting for a spayed female would be best bet.

He’s a rex, are there any breeds that don’t usually get along (or usually get along really well), or does it completely depend on the individual rabbit? Should I keep it within the breed and look for another rex?

Breed, size, age doesn’t matter at all. 🙂 It’s really about the personality of the rabbits, and their personality around humans also really doesn’t reflect how they will be with other bunnies. Rabbits who have been bonded before or lived in a group of rabbits often seem a bit easier to bond.