Well, there are two trains of thought I can think of on this question.
1. Is it OK to buy a gun for a teenager? I grew up in Alaska where guns are very common. I started shooting literally before I can remember (probably around age 4 or 5). Before the age of 8, I was shooting high powered rifles under adult supervision. By the time I was 16, I think I had 4 or 5 long guns already. I owned real guns with real bullets. I hunted unsupervised once the law allowed me to do so. I have yet to kill or hurt any human with a firearm. However, despite my extensive knowledge of firearms and being mature for my age, during my fragile teenage years, I did find myself becoming lax about gun safety. It's not that I am stupid or I was intentiionally being careless, it is just sometimes you get caught up in the moment and forget about being safe.
Is it OK to buy a gun for a teen? I would say yes. However, if he has yet to be exposed to firearms, I would keep a very close eye on him. Lock the gun away (even a BB/pellet gun) when not in use in a safe or with a trigger lock.
2. More general...should you buy your teen something they want...
Nothing makes me cringe more than the words "I want". I beleive that the standard of living has increased dramatically for most Americans since their childhood (when I was growing up, a 2400+ square foot house, several cars, 4 or 5 TVs, McDonalds 3 times a week, and a house full your favorite toys (be it firearms, cars, golf clubs, or whatever you want as an adult) was unimaginable). As a parents, most of us want to give our children more than what we had. I find myself falling into this trap.
I would say that you could potentially make this a good lesson in life for your son. Make your son work for the rifle. You can either give monetary credits to your son based on criteria he meets or make your son go out and get a job (by the age of 15, I was bussing tables, washing dishes, waiting tables, cooking, or doing whatever job was needed to be done at a local restaurant. Eventually, by the time I graduated high school, I worked my way to a chef...all for $0.75 above minimum wage).
As far as giving your son credits...lay out dollar values for actions you wish to encourage in your son. If you want him to get good grades, make an "A" worth $3 each, "B" $2 each, and a "C" $1 each. Your son mows the lawn? Give him credit for $5. Keeps the house spotless? $10 a week. Changes diapers? $0.25 each. Roofs the house? Buy him the rifle. Mandate that at least 25% of the credits you give him must come from grades (or whatever percent works for you).
I'm not sure how much you are looking to spend (some pellet rifles can run up to a few hundred dollars). Adjust your values accordingly (if he want's a $30 rifle, then I'd give him less money for most things).
Children need to know that things will not always go their way. Outline a plan and sit down with your son and tell him this is what he needs to do to get from "A" to "B" to get his rifle (Hunter's Education is a great idea BTW). If they don't like it? Too damn bad.
You can try to change the deal a little bit to try and teach your son to aim high and be persistant at accomplishing a goal. If he is willing to work for the $300 mark, let him know that you will by him a 22 rimfire rifle, a scope, and a membership to a local shooting club rather than a pellet gun.