In terms of what rabbit breed would be best, there are no valid patterns in bonding success nor temperament that is going to make one breed better than another. Any breed is going to probably have equal variability in bonding compatibility, as it comes down to your rabbit’s personality and the personality of the other rabbit which ultimately defines whether a bonding will eventually be successful.
If you get another rabbit and spay/neuter them, this guarantees you don’t get pregnancy– that’s the only guarantee. It is possible he’ll be very aggressive and hump both males and females (humping is a dominance behavior; females do it too– it’s not just a mating behavior), but that possibility is there regardless if he’s neutered or not actually. What makes bonding with a hormonal rabbit notoriously difficult is that there are strong hormones backing up the aggression and mating needs, and that’s typically something that cannot be diminished via the bonding process as we see with two fixed rabbits. Additionally, the presence of a hormonal rabbit has been known to bring about hormonal behaviors in fixed rabbits, so even if your rabbit is ‘chill’, other rabbits may react in ways that will also make a difficult bond.
As someone who volunteers for a rescue, I’ll also say it will be difficult for you to try and adopt a rabbit if you inform them you plan to bond them with your unneutered rabbit– the foreseen difficulty/plausibility of a bond forming, and paired with that the likelihood of trying to return the adopted rabbit, is perceived as high, so you may be turned down by rescues.
I would suggest a dog/cat. In terms of which is ‘better’, I do not know, but there are articles online for both in terms of best way to introduce them and what temperament you want in the cat/dog (ex. evidence of low drive, such as not chasing squirrels and birds).
The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.