In a sanctioned league you can expect to pay from $12 to +++++ whatever. The higher priced leagues will more then likely be scratch which means no handicap to level the bowlers' skills within the league. If you are just starting out in league play, I'd make sure you join a handicap league. There may even be a learn to bowl league that provides coaches to assist in learning the game. Since you have not bowled in league before, you will be asked to pay for sanctioning fees to USBC. That's a yearly fee that will provide you achievement awards, general rules to follow, prize money bonding (you want this), and creates an official average for use in tournaments of all kinds and levels.
In all leagues you have a typical break down of the weekly fees. Say a league is $12 a week. You might be paying $9 to the house for lineage, $1 to the secretary/treasurer and $2 to a prize fund. A prize fund that will grow throughout the league term and be awarded at the end in pieces and levels of achievement. Like most improved, high average, high series, high game, high handicap series and high handicap game as well as team placements. In some leagues that prize fund has to go a long way and the payouts are minimal, others pay more. Depends on how much of your league fees go into the prize fund.
Most centers have a league co odinator. Ask the center about their leagues and some that would be good for you just starting out.
Erin