Do show up early. There will be paperwork to fill out.
First lessons are always a little awkward as you don't know anyone you need to do this business stuff and as a beginner (or even a more experienced rider) you don't know the drill.
Just show up early and bring a good attitude. Most places require helmet and shoes with heels. No this doesn't mean high heels. Most places will at least provide helmets but if you have your own awesome. It sounds like you do and I'm a little surprised as you say you haven't ridden before? If you have a fitting certified horseback riding helmet awesome, if not that is what you need, no bike helmet. Wear jeans or yoga type pants assuming you don't have riding pants.
If you want a tour ask for one *at their convenience* but I would expect one in the traditional sense- you should be shown all the stuff immediately relevant (I would have people walk with me and talk them through what I'm doing "this is where the brushes are" etc) but not a traditional tour of the property. I say "at their convenience because a busy lesson barn may not be able to provide that, if you want the traditional tour and to talk more broadly make an appointment before hand to tour the farm, a good farm would be happy to oblige.
Depending on the barn/schedule/time or general business I would either expect to groom or to have the horse ready. If you want one or the other this is the time to specifically say "so this is great but for next time I would like to try "x" if possible" (DO try and groom your own horse, the only way to do this is all the way!!). Then you will go in and ride, see first part of the paragraph you may help "undo" all the stuff after- cool the horse out/untack/brush etc.
It really depends on the barn and if you have any questions or want to try something different next time ASK!! I would definitely expect the staff to be reasonably accomodating or have a good answer why not (you may not be allowed to get your horse out of a group pasture for safety reasons for example). Do expect to be babied at first they don't know you and you are a beginner, but baby should be more "mentored" then pushed aside, this is supposed to be enjoyable and a learning experience which goes far beyond riding.
Riding is hard and possibly dangerous work, while you may trot or do offline work a good instructor will make sure you are solid in the basics before pushing you ahead. Don't expect too much too soon, that's a good thing, a good instructor will keep you entertained though, again this is supposed to be enjoyable (I just put this as some people are all "I've ridden 3 times why am I not jumping 3 feet").
Just communicate. I know I loved when people talked to me and if someone wanted to get on and get off fine, but if someone wanted to learn all about the horses (including and esp obscure "researching" questions ;)) and help as much as possible I would definitely encourage that as much as possible!!