AV covered it. Bicycle Sportshop is prettymuch it for rentals. Barton Creek is a huge network, but I would call it intermediate-advanced once you get off the main trail that follows the creek. on the weekends, the main trail gets packed with hikers, dogs and dogshit. be prepared to cross the creek several times if you want to do the main trail.
based on stuff you've posted, I would recommend either Pace Bend or Muleshoe Bend. fun terrain, ease of navigation. last time I was out there, anyway. plus I think they still do XC races at PB so it has a well defined loop, as does Muleshoe. both are about an hour drive to get there, though. but there's a pretty decent bbq place (Opie's) right near Muleshoe.
I've never been to Rheimer's, so I can't say anything about it. same for Slaughter Creek, but for what I know about it from a buddy who lives out there and rides it with his young son, it's probably too far to go for not much trail.
Brushy Creek is probably also a hike for you, but is a good option. it has a wide paved path down the middle of it, with the creek on one side, and a hill on the other for the whole length. Deception is on the hill side. there is a trail that runs along the creek with lots of technical options, but is generally just fast, flowy hard pack. there is a flat loop between the sports complex entrance and Parmer Lane, bordered by Brushy Creek Road. you can probably get 10 miles without messing with Deception (which really isn't that bad---just rocky).