Katie, my standard recommendation is to keep as few roosters as you can and meet your goals. It’s not that you are guaranteed problems with more roosters, just that they are more likely. The only reason you need a rooster is if you want fertile eggs. Everything else is personal preference.
You’ll often see magic numbers quoted on here for chickens. One of those supposed magic numbers is hen to rooster ratio, for full sized fowl often quoted at 10 hens per rooster. I’m sorry but there is no magic in those numbers. You can see hens barebacked or acting over-mated with one rooster and over 20 hens. Breeders regularly keep one rooster with one or two hens in breeding pens for the breeding season and don’t have those problems. If roosters are going to fight it doesn’t matter if there are 50 hens or only 1.
Two or more mature roosters can live with a flock and often do, but you normally need a lot more space when you add a second rooster. You are dealing with living animals so behavior is not always consistent, but normally two (or more) roosters will determine which is the dominant one and then split the flock into harems. Each rooster claims a certain territory so they can avoid each other during the day. If you don’t have enough room for them to claim territory and stay out of line-of-sight of each other your potential for conflict goes way up. Normally doesn’t mean always but more space is a lot better than less.
That’s for mature roosters. Many people make the mistake in confusing pullets and cockerels for hens and roosters. They are not. The cockerels have hormones running out of control once they kick in and no self-control. The pullets don’t mature as quickly and don’t have a clue what is going on so they resist. The cockerels are bigger so force is used. Once they mature into adults things normally settle down but watching adolescents sort this out and go through the maturing phase is often not for the faint of heart.
I don’t know what your goals are but since you only ordered one rooster I’d think one just might suit you. I know goals change though. Good luck with your decision.
In addition to Sour’s comments, another sign or over-mating is when the hens or usually pullets stay on the roosts during the day or somewhere the cockerels or roosters have trouble getting to them.