If it were just me getting the membership, it would be all about the golf course & the value.
But 1484, you're talking about a family membership with 3 kids. That introduces other dynamics -
They got a nice pool? Junior golf programs? Spa? Restaurant?
It's basically going to be your family's social outlet.
Lots of great advice so far and I very much agree with the above. At a private club you're basically paying more for convenience and better course conditions. The ability to hit balls or play 9 after work. Place for the kids to drop off the kids and have them do golf stuff in the summer. There are a ton of great deals out there right now, depending on where you live.
1484, if you're going to playing 60 rounds during the year I think it makes sense, especially with five golfers in the household. Invite the guys from work play on guest days or member/guest tournaments. My parents and my family are members of the same club here in San Diego. They have dinner at the club at least two nights a week, one of those is with our boys and they've made some new friends. My Dad also plays four days a week so he def gets his money's worth. I'm on a junior executive deal, all the same amenities as everyone else, pay much less but don't have any voting rights.
Ask about the financial stability of the club. A lot of places with no initiation and attractive packages are in bad shape financially. Get ready for assesments. If you can find a club that fits your needs and is stable, that is a great way to go. If you are like me, and are more interested in golf than the social aspects, there may be better places.
Agree, ask when the last assessment was, how much it was. If there are any plans for renovating/repairing the golf course or clubhouse. Any major issues with the golf course. In California there can be an issue with having enough water or problems with course conditions with older golf courses that were built on clay. If you have a chance try to talk to some other members and see how they like the club.