I play in an 18 hole golf league in the Austin area. By the rules, no gimmies, play as it lies (unless weather makes it lift-clean-place).
If playing individually, and to grow the league, you almost have to have the rounds handicapped. The league I play in offers players the ability to enter gross games, net (handicapped) games, skins, eagles, etc.
The better players play in both, the higher handicap players usually just play in the net. We'll have up to 30 players compete each week with handicaps ranging from +5 to 30. It's really fair and extremely enjoyable. The people who run the league (in their spare time!) have put a considerable amount of time and effort into it and that has to be one of the main reasons everyone gets along.
By all means, if your group of players are all in the same skill level, than you could do a just skins and gross game and call it a day.
If maintaining amateur status is important to players, than they could play just the skins (skins can be paid in cash and not affect amateur status since skins games are considered gambling) or have the option to win gross or net game proceeds up to $750 in gift certificates and not cash.
Depending on how big your group is (and technology capabilities), you may want to try having an online leader-board like www.scrolf.com or Golf Game Book. Makes it very easy to keep track of scores, who is leading, skins, etc.
I would also highly suggest having a 3-person "rules and operations" board to settle any arguments, decisions, etc.
The key to leagues is communications and consistency, so just as long as you keep it fun, maintain some bit of the "edge" that competitive golf creates, and maintain fair rules you'll have a successful league. Try to smooth out rule changes over a few weeks instead of all at once so players can become adjusted to changes.
You'll be very surprised at the amount of golfers out there who used to play in high school or college who want to play competitive golf. It's really helped my game improve because all of a sudden every shot counts again.
Good luck!