I have a collegiate bridle and I just use the regular braided reins that came with it. I can say that I HATE rubber reins though. I just use the same bridle for schooling and shows. I take care of my stuff, so it lasts a very long time. I have one bridle that I have had for 7 years, and someone asked me if it was a new bridle the other week
I got a pair of the cheapest reins Dover offers last year for my qh: Dover Saddlery | Suffolk Web/Rubber Dressage Reins . for schooling... This year I got another pair for my paint! I don't know why, but I really like them. I have laced reins, smooth dressage leather rein, and I got Thinline reins to try (return them back after 1st try), and this cheap ones are the most flexible and non-sleep out of everything I tried.
I use the same for schooling and competition; red braided rope reins I got from Tractor Supply. I can't STAND rubber reins and am mildly annoyed by leather. The rope ones have a nice... Feel. It's hard to describe, but they just fit more comfortable in my hands.
I personally dislike braided reins, they always ended up coming apart on me, the braided parts would unravel....but that's probobly because they were cheap? But the reins I absolutely do love, and wont use anything but are these:
They are Rubber Lined Eventing Reins - I have a pair to go with every bridle I have.
I do have other Rubber Reins - Pink, White and Baby Blue. But those are more for fun.