There isn't really a formula like you're thinking. Cats of any gender in whichever ratio can get along just fine. I think what matters more is the personality of the cats, and then age.
I'd say litter mates, or kittens that have been together from a young age have the best chance of getting along well and would probably end up enjoying each other's company. If you're sure you want three cats, You'd probably have the best chance of getting a group that gets along with the addition of two young cats who have already been raised together. Of course, doing so would mean going through the crazy kitten stage with three cats all at once. One kitten can be a lot to manage, but three together can be much more than 3x more naughty.
Cat's of other ages can get along great as well, though. I've had cats young and old that have been good buddies. My cat Trixie (RIP) was always at odds with the first 2 cats she lived with, but she was good buddies with a kitten and several other cat's, young and old, that she lived with after that, and this was when she was in her teens. She never did like Cheddar, though because Cheddar was way too rambunctious for her. It just goes to show that cats get along better with some cats more than others depending on their personality, and age doesn't always have anything to do with it. You should consider temperament and activity level as well.
Are you sure you want to go from one new cat to three all at once though? Have you had two or three cats at the same time before? How much space do you have? I have had 3 cats at once, and several times I have lived with 4, but I find that 2 at once just works out best for me. With more than two, the dynamics are more complicated, food and vet bills cost more, more scooping the litter box, more housekeeping, etc. Three cats can be great in the right situation, but if you haven't had a multiple cat household before, maybe you want to start out with just two?