As a 5-gallon-batch brewer who bought one only to buy the other after struggling for two or three batches, skip straight to the 10 gallon.
Your efficiency is gonna be disappointing for the first few batches, which will lead to bigger grain bills to hit your gravities; you're gonna have to add hot or cold water to dial in your strike temperatures until you get used to your system; you're gonna learn that "stirring like it owes you money" is a somewhat sloppy procedure that benefits from a few inches of extra space at the top of your tun; etc.
As for the braid, I made one, it worked pretty well for batch sparging six or seven batches (only one stuck sparge), then it collapsed and had to be repaired mid-mash, which sucked. I got a 6" bazooka screen, which is made of stiffer stuff, and seems to be working out well so far, but it's only been one batch. *shrug* Don't get the 12" one, though, at least if you go for the round cooler; when you factor in the bulkhead, it's just a little bit too long (another lesson from hard experience).