I'll preface this by saying that I know almost nothing about lawn care, other than using a lawn mower.

We just built a house and it was completed in March, located in the Birmingham area of Alabama. The builder put down winter rye covered with this straw netting stuff, mainly for erosion control and to establish the soil until we determine what kind of permanent lawn we want. The ryegrass is grown in, although patchy in spots, there are some bare areas still. Lawn is probably about 2000 sq ft or so.

I'm wondering about the best way to approach the permanent lawn. I think we just want to put down some kind of seed, but I wonder if sod is the better way to proceed.
*Should I wait and let the ryegrass die off when it gets warm before we take the next step, or is now the time to start?

*Do I leave this netting stuff down and seed over it, or is it necessary to pull it all up; seems like it could get stuck in the mower unless I always mow really high. I've had people recommend both leaving it down and it will disintegrate, or that I should pull it up.

*Any recommendations on best type of grass? Several people have recommended Zoysia to me, and I've found some seed, but I've read where it usually does better with sod. I've also had people recommend tall fescue or bermudagrass.

We've got kids and want a lawn that will stand up to our climate and kids play. I've seen lots of good info on here, but nothing that seemed to apply to this situation. I appreciate any advice. I've seen so much different info, it's hard for me to decide the steps to take.