How do I go about getting the roosters introduced? I've read there will be fighting, which I'm not a fan of but also understand there has to be a pecking order. Is there too much fighting? When should I be concerned?
I would probably start by having them separated by wire mesh (adjacent pens, or one group in a pen and the other group free ranging.)
If they try to fight through the mesh, it limits how much they can injure each other. Hopefully they can settle matters by bluffing through a fence, and not have to really fight later. If they keep fighting through the mesh, I would not let them together. If they reach a point when they wander away from each other and do their own separate things in their own spaces (when there is still mesh between them), that increases the chance that they will also do their own separate things when turned loose together, rather than fighting.
If they do start fighting, I do not know exactly when you should be concerned.
Ruffled feathers and staring at each other are safe enough, usually with a bit of jumping around and wing flapping and posturing.
Drawing blood is quite likely (combs bleed easily). Comb injuries are not really series, but injuries to other parts of the body can be a bigger issue.
Depending on how long and sharp their spurs are, they may be able to do a lot of damage to each other, or they may not. (If they have sharp spurs, you might consider filing the ends to round them a bit, before letting the roosters together. That makes them less likely to cause major injuries to each other, or to you if you are trying to separate them.)
If one tries to get away and the other keeps chasing him, you should definitely separate them. That situation can lead to the loser getting badly injured or killed.
If one walks or runs away and the other lets him go, that is great. They have established who is the head roosters, and the other one will try to stay out of his way. But do keep an eye on them in case the loser tries to challenge the winner later and fights longer, and they do need enough space for the loser to stay out of the winner's personal space. The amount of space they need may be too big to share a coop, but sharing the whole yard is probably big enough.
I don't have personal experience with roosters fighting past the "bluffing" stage and maybe an occasional ripped comb.