I would just get there when it opens at 11. There may be a small line but nothing too bad. If you want to be safe, 10:30. If you get there at 1 on a Saturday you wouldn't have an issue getting food (Saturdays they order more meat and are open for longer) but you will have a line. On the other hand they only stay open until 3 or so on Sundays so you run more of a risk of running out of food.
Lockhart's won't have too bad of a line. Slow Bone in the Design District is solid. Baby Back Shak is the best in the downtown area. Sonny Bryan's is a well known place which is good in a pinch but I wouldn't go out of my way to get it.
As far as portions at Pecan Lodge, they're solidly sized but not huge.