A lot of your questions can be answered by talking to your instructor, if they are good at their jobs, that is! It's never a bad idea to get a second opinion, of course :)
As far as age/breed goes: Any horse of any age can be calm or spirited. I've seen 25 year olds that are spirited and hot and spooky, and then you get some 5 year olds that are **** near bombproof. Same goes for breed - there are QH that are hotter'n'hell, and there are TBs whose favorite gait is "whoa."
A lot of it is going to depend on your experience and comfort level. When I was your age, I was the guinea pig - my instructor tossed me on anything and everything. Others my age were more timid and didn't want to ride anything too "up" on themselves. Still others were even crazier than me and had no fear. My first horse when I was 12 was a green broke TB mare.. probably not the best idea in the world, BUT I had a competent instructor that brought us both along.
My personalized suggestion for a first horse for your age range is to get something really well broke that you can have fun with. (With my first horse, I was on guard the entire time I was around her for the first year and a half). I'd suggest nothing less than 6 years old, personally. Breed depends on what you want to do as well - if you want to compete in breed classes (AQHA) obviously that's going to limit you. Otherwise if you want to dabble in everything, you can go with almost any breed. Bloodlines become important when you are 1) breeding 2) buying a young prospect and 3) wanting an indication of potential performance, usually for upper levels of competition.
When you're looking to buy, take along your instructor or a knowledgeable person to help. Always get a PPE for soundness, and always ask if the owner would mind if you request a blood test for drugs (I've never done one, but you can get a feel for a person's response.) I do suggest going to try the horse a couple of times to make sure you're the right fit for one another.
Ask questions. Lots of questions. Especially if some things are super important to you, such as ground manners, clipping, tying, bathing, trailering etc. If you're wanting a companion to go trail riding on every weekend, you may not want to get a horse that hates to trailer.
Boarding is a regional thing. I pay $400 for a paddock, but that $400 will get you a stall at a barn an hour away. In some regions, $150 will get you full care stall, and in others, a stall runs you upwards $1500/month.
Do as much research as you possibly can - as you obviously are doing :) Good luck with your search, and HAVE FUN!
Horse sales sites that I like
Also, search Facebook for horse sales groups in your area - I've found some amazing horses on FB that aren't listed elsewhere..