Wear your helmet with pride.
I’m one of the few WESTERN riders that wears a helmet in my neck of the woods and I wear it for showing too.
If you already have jeans and traditional western boots, I would wear that. But if you would like to get your feet wet and make sure you like it first, you can wear paddock boots and half chaps with your breeches. It’s fine - who cares.
And truthfully, if any trainer is UNprofessional enough to make a snarky comment about your attire, then you can find someone else.
That’s one of the reasons why I will never go back to a particular English trainer in my area. She was dissing barrel racing left and right at my very first lesson with her and it was very clear she had no clue about it whatsoever. Very unprofessional, IMO, and I will take my business elsewhere.
I guess some of these questions ultimately depend on who you end up taking lessons with and where.
For example, the reining trainer I take lessons from / ride with actually has a normal full time job away from horses. And he primarily trains horses for people so he’s almost always got different horses in his barn that he is riding and working with. Obviously, those horses won’t be up for lease! But they do have a few of their own horses that I know he has people ride sometimes for lessons.
Other barns might be different and they may or may not have horses available to lease.
How about your own horse? Just because it’s a hunter/jumper, doesn’t mean it can’t learn basic reining maneuvars!
I grew up riding Western and only have recently taken lessons here and there for English (to do my local hunter events). And I feel like reining progresses FASTER than any English disipline will. Not that that is a bad thing one way or the other, but I know my English trainer waits a very long time to actually ask a horse for a flying lead change … whereas my reining guy might ask for one the first day he gets on a new horse, if he thinks the horse can do it.
So maybe that’s my only advice comparing to the two. And maybe I"ll be totally wrong, but you might feel like the reining progresses fast in comparison to what you’ve experienced on the English side of things.