You might want to check out a blog by this guy I found. You'll find it by searching "Horse Crazy Bob Goddard" on Google, clicking on the appropriate website (probably the first) and then clicking "Bob the Equestrian". He is also an older beginner male rider and quite funny! He has an advantage over you though, since he was introduced to the horse world through his daughter/s.
What should you expect when you begin lessons? Every instructor is a little different. You might be expected to learn to groom and tack up, or this may be done for you. You may have a mostly ground lesson the first time, or be put on the lunge line, you may just hop right on. Most likely the most advanced thing you will be doing in your first lesson is some cone or barrel weaving on a school master.
If you really enjoy riding, I'd advise you to get a helmet, paddock boots (as they are much cheaper than tall boots) with the proper heel (usually described as 1 inch, anything made by an actual horse company is usually good to go though), and gloves. Gloves help prevent the reins burning your hands, keep your hands warm in the winter, and help keep your hands feeling nice when doing barn chores if you end up participating in them.
Pfft, you're just scared all those 12-year-olds would show you up
. (Just kidding)! Most instructors do not specialize in adults, I'd be surprised if you found anything like that since the riding market seems to be more centered toward children and teens. But almost all instructors do provide private lessons (beware though, that these are often more expensive and shorter in length than a group lesson. If you plan to show it's a good idea to get one or two group lessons for the benefit of being able to maneuver in an arena with many different horses moving in it). Most people think they progress faster taking private lessons, which is a plus.
When looking for an instructor, it's important you're open-minded but not willing to settle. If you stick with the wrong instructor you're just going to end up wasting time and money when you could be someplace better, and end up with a bunch of bad habits which take time to break (trust me on this one). What you want in an instructor depends on your personality- perhaps you're quiet and don't want anyone too loud, perhaps you're really clumsy and kind of dense and want some one with a lot of patience, etc.
Personally, I love it when I see male riders, even older ones. I know a lot of other female riders think the same way. It's pretty rare now in a lot of places to see a male rider and it's refreshing when you do see one. If you're single you won't have any trouble looking for potential dating prospects
(because there are also older women who ride, even beginner ones)! You're probably going to be teased, but if you have a good sense of humour about it you should find that the barn will provide a few good friends.
Good luck and have fun! Remember not to care what anybody thinks and to kick butt and take names!