Yea, I'd use cat6 now not cat 5, but it's easy before the walls are up. Pick your drop location wherever your network connectivity or server closet is going to be, and run ethernet drops from every room into that spot. Me personally, I would run multiple cables to each drop, at least 3, so that when they inevitably go bad you already have backups there.
If you are feeling really enterprising you might run ethernet to two spots in each room so that depending on how they arrange the room the network won't still be too far away.
You want to go do it when the walls are framed but no drywall is up yet. Should literally take 5-10 minutes per run at this point since you can just go through stapling brackets to the wall studs to run your cables.