I had braces. I'd actually recommend that you wait. Of course, then you run the risk of not having the money to pay for it or not being covered on insurance, so it's up to you. I had really crooked teeth when I was a kid, so I got braces when I was 12 or so. They were taken off roughly 2 years later, but I had to wear retainers until I was 18. One (the bottom) was supposed to have been permanent, but it fell out. The other, (top) I just wore at night. I followed all of the rules to the letter. No caramel or popcorn or dark soda or anything. I brushed my teeth six times a day. I was extremely preoccupied with making sure that I didn't get permanent braces marks on my teeth.
In college, my wisdom teeth started giving me problems. All four were impacted. There was no room for them. They pushed against my other teeth. They hurt. I had them taken out. Now, as a result, my teeth are kind of crooked again after having gone to all of the time and trouble (and my parents' expense) of correcting them. It's not bad enough for me to want to go get braces again, but it is very noticeable. With that as my experience, I'm gonna say that if your teeth aren't really all that bad, wait until after your wisdom teeth come in (or don't) and wreak whatever havoc they choose on your mouth.
As far as whether or not it hurts goes... well, yeah. Again, my teeth were really crooked, so it might be different for you. I had appliances and rubber bands and everything but headgear, man. Getting them put on doesn't hurt all that much. Adjusting to them does. And when they tighten them every month, it sort of feels like you've spent all night grinding your teeth. It was manageable pain. It was really a more annoying type of pain than anything more dire. In addition to that general ache, the little metal brackets will sometimes rub up against the inside of your mouth and cause sores. The occasional rubber band will snap. It wasn't the most painful experience of my life, but it wasn't fun, either. All in all, I'd say it was worth it in the end. I wouldn't let the pain be the deciding factor, because while it does hurt, it's not usually a huge deal sort of hurt.