I shoot in two Bullseye leagues and also compete in a number of other types of matches over the course of a year. Here in Massachusetts, the teams are generally fielded by the various gun clubs. Each of the leagues I shoot in has around 8 to 10 club teams, with perhaps 6 or 7 to as many as 20 shooters on each team. In formal (and I use the term loosely - it's really not very formal at all) competition, the top 5 scores for the evening "count" against the top 5 scores from the other team. That allows everyone to have a good time and not worry about their score screwing up the team's aggregate if they're not that good a shooter or just have a bad night. Obviously, with that system, more shooters on the team is an advantage, all things being equal.
We shoot the NRA Gallery Course - 50 ft, .22 only, 10 rounds each of slow (NRA B2 target), timed, and rapid fire (both on NRA B3 target). A perfect score would be 300. In our recreational league, scores in the 260s are respectable, 270s quite good, 280s very good indeed, and we very rarely see anyone break 290, with one exception - we have one shooter who is an NRA Master level shooter averaging over 290.
An alternative to trying to set up a league, which requires getting a lot of people on board, would be to get a small team together and compete in a postal league, where you score your own targets on the honor system and mail (hence "postal" but it's email now) your scores in. I compete in this one:
www.ierpa.org which is based in the Pacific Northwest but accepts teams from all over the country.