I do alot of reining so here are some tips.
1. Think of dressage the movement and feeling it is very much the same.
2. Don't lean back to far this is a mistake I see to often in riders so sit up!
3.Relax you will start to drive the horse nuts if you tense up. Just hang loose.
4. And the most important your first lesson will be hard but it will only get better. Look at the lesson as a challenge your just trying something new.
Hope this helps
I agree with this. You want your seat to be back but there is a reason why you see so many hunchy reiners. It may not look pretty but it works at least with regards to stopping. Equitation doesn't matter much, well it does to the degree you need to be functional but the style you take on doesn't matter as long as it works (your coach will probably have a preference).
It's like jumping vs. hunters. Equitation is needed in hunters and its pretty, but jumpers tend to be more functional in their riding and a little less pretty. Same with WP and HMS, horsemanship is prettier to look at, but your position in pleasure is probably a bit more functional. Not that HMS and hunter riders on function, but my point is it tends to be more pretty than functional.
I think equitation as a base isn't a bad thing because it makes you a stronger rider, you do have to adjust a little bit.
I'm really glad your taking some reining lessons on a finished horse, this is going to benefit you a lot in the long run.
Also in reining, at least for me I keep shorter stirrups, not englishy but what I would have for western horsemanship. It lets me feel the horse a little better I find. I'm taking dressage lessons right now and I'm finding the stirrups are longer than what I ride my reiners in, its more like my WP stirrups ahha.
The more important part of your first lesson will really just be getting the feeling. Depending on the coach you may not get to things like sliding right away, you might out of say a trot. Again that depends on the coach. You'll probably feel like your legs are sitting so far forward on the horse compared to english, but really its fine.
You'll love it! It's very addicting!
Just relax and have fun. It's good your challenging yourself it makes you a better rider.
Let us know how it goes :)