It would be worth your while to find an archery shop that knows something about traditional archery if you can. Whether you end up shooting a longbow or a recurve is solely a personal preference, and there are about an equal number of people on this website who are passionate about each. The only way you will find out which one you are passionate about is to shoot them both. And after you buy one, you'll probably change your mind again, and maybe again later on, until you settle in on one or the other.
I would recommend that you buy a fairly lightweight bow, maybe 35-40#, to start with, because it will make it so much easier for you to learn good form. You can find these bows new or used from $100 - $200. When you grow out of it, you can sell it and get most of your money back, or keep it around for people to shoot who come visit you, or for your kids/grandkids, etc to shoot.
They can measure your draw length in an archery store. If you are new to traditional archery, your draw length will probably increase by an inch or maybe even more as you learn to use your back muscles and expand through the draw.
The best thing you could do is to find a coach to get you started in the right direction, or if you can't, attend a hands-on class by someone like Rod Jenkins or Rick Welch, or if you can't do that, at least buy Masters of the Barebow III DVD, and study Rod's section of that DVD, or Rick Welch's DVD, The Accuracy Factory.