Well I don't know which ones to buy for a mini but since no one has answered you I'll give it a try.
I'm assuming English girth because you said leather but clarify me if I'm wrong. I'm not at all wild about the nylon with fleece types, the fleece tends to roll easily on my big horses and I can't have that, my little cutting bred QHs are way too quick and from what I know of any small equine the smaller they are the quicker they tend to scoot.
I'd also shy away from the neoprene types as well. They don't last long. Unless it's brand spanking new, it ends up cracking within months and then pinches the hair, and even when it is new it can cause sores on the ones that have thinner hair that it doesn't eventually end up pinching. If you can find it, go with felt vs fleece, leather vs neoprene. I personally prefer a nice felt girth (usually nylon reinforced but what touches the horse is the felt) soft on my sensitive horses yet enough 'grip' to keep the saddle in place but I'm not sure if they make them in the English type. I know I had a hard time finding them even in the Western types, the last time I tried to buy and it's been years since my English saddle was usable. They just started making them again for the Western girths. Worse case, they do sell those little converter straps that will make a western girth into an English one. I know you can get some pretty tiny mohair western ones, I'm not as wild about those but I'd definitely take it over fleece and neoprene. You might have to go extra short or try to fashion a converter yourself? I dunno, just some thoughts.
Also caution on the Pro-Choice brand of girths specifically the Western ones but I'd really be cautious on the English types too...my dad just had one, less than a year old, barely used, that the buckle broke! He's lucky he didn't come off as he was loping a young horse at the time. No signs of wear, the metal was shiny and new looking, it just broke, clean in half. In all my years of riding, I've never seen a Buckle break like this! EVER. We have always worn out the material vs the buckle. We usually re-purpose those dang buckles, they last forever...but not so with that Pro choice one. I emailed them about it, and they ended up forwarding me an internal communication between the employees, one I believe was a big error as I certainly would have never said that to a customer!! Apparently it's an ongoing problem with them.
My 12 hand Curly Pony Mare takes an 18" girth with our http://www.thorowgood.com/safari-Cub.html Saddles. My mom actually made a 10" girth for our B Sized mares due to the billets being so long on the saddle. We also have 18" and 12" Western Cinches as well for the mares with the western/english adapters for the saddle.
The best thing to do is to find out your horses heart girth and then the length of the billets on the saddle before ordering or buying a girth.
Thanks guys! I ended up ordering one of those fleece lined ones only because I couldn't find any other english ones. I'm on the search for a leather one though. I figured I'd just use the nylon/fleece until I can find something different to replace it with.