My wife and I fly Southwest a lot. It's inexpensive, but remember that there are NO assigned seats. Check in online 24 hours before your flight and as close to the flight time as possible -- say you're flying on Tuesday at 11 a.m., so you want to check in on Monday as close to 11 a.m. as you can. Get them all checked in at the same time and they're more likely to find seats together.

Check also on the policy for families traveling with children under 12 years old.