RE: small gun bigger than .243
I'm going to come right out and suggest a lot of things, I've owned/operated/worked at/instructed at a dozen rifle ranges in my limited time on earth, I've seen and learned a lot about new shooters.:
FIRST OF ALL, you're 14, if you're average height and weight, and not a wimp, there's really no reason you should be terribly worried about recoil, two or three years at most with a little practice and you'll be big enough to handle any recoil out there (barring safari cartridges which take some getting used to), there's not a lot of reason to need a "small rifle" at your stage, two or three years ago, yes, you'd need one, but like I said, you'll grow out of your recoil problem in the next year or so-if you have one at all now....the first deer rifle that I owned was bought for me at the age of 12, a .30-06 Ruger M77-II standard, I've never had a problem with it and was shooting a .416Rigby for targets by the age of 15 (family tradition with .416Rigs, we've all got one or two for one reason or another). My sister started shooting a .308 when she was 11yoa (about 75#), I started dating my fiance when she was 14, let her hunt that year with my .300win mag, My sister is 15 now, and she's moved up to silouette shooting with a .45-70+P marlin 1895. My fiance is early 20's and under 120#, she took her first buffalo with a .375H&H this winter....
Secondly, there is no sporting rifle that kicks so hard that you can't add weight or pads enough to tame it enough for a 130-140#man, like I said, I've seen a lot of people start shooting, and there's nothing more stupid that someone coming to the range without some sort of recoil pad, I don't care if it's wimpy or not, when it comes down to it, if you need a pad to be a good shooter, there's nothing to disrespect about using one...my sister and fiance can handle those rifles because I've weighted the forends, cut the stocks to fit them and added recoil pads (most are butt mounted, but slip ons work if that's what you've got)...having a gunsmith add weight and a pad will cost about $20 unless he's a crook, or you can do it yourself if you feel comfortable with it.
I'd recommend to you what I do all new shooters (adults that is), get a .308win or a .270, they aren't terribly hard recoiling but they'll do the job as good as anything else, plus, you don't really out grow your rifle, if you buy a .243 just because it is light recoiling, in two years you'll be able to handle a .300win mag or bigger and probably wanting that type of performance by then too, and you'll have to buy another rifle, start out with one of these (or countless others) and you avoid this step later.
One thing people often do that is really stupid when starting off, they'll give a kid a compact rifle in a "real cartridge" because it's smaller so it'll fit them=easier to shoot...you couldn't be more wrong, you want the rifle to fit the kid, but it's either got to recoil less or it's got to be weighted a lot, take weight out of a rifle and it kicks more, I've got a 4.8# .300WSM custom made compact that I don't even really like shooting without a shoulder pad, my little 9yr old cousin that it fits great, but it'd kick the hell out of him if I let him shoot it...it's just too light.
If you're on the small side for your age, or you honestly do have a problem with recoil, then by all means, don't take the above advise, I was always shorter than everyone else, but I've always been very muscular (putting up hay all summer and feeding it all winter tends to do that to you), so I wasn't necessarily any "smaller", just shorter and lighter.
Don't discount the .243win, there's absolutely nothing wrong with hunting a .243win, I've hunted them for deer and elk, taken a 238# (live wt.) doe at 267yrds, it's quite a capable round if you shoot it well.
If you are on the small side, here are some other recommendations:
.44mag or .30-30 in a levergun-Marlin only, both are quite capable hunting rounds to 150-200yrds, assuming you put the bullet where it needs to go-the .30-30 is flatter shooting, but the heavy bullets of the .44mag are quite potent even at long ranges and low velocities...the .444Marlin is also a good choice, a little more stank than a .30-30, but with the big bullet capabilities of the .44mag, I've used one on deer out to 257yrds to good results.
.257robers, 7-30waters (7mm bullet in a .30-30 case), 7mm-08 (7mm bullet in a .308case), .250, and the list goes on and on, .25-06....
7.62x39mm (SKS rifles shoot this, very light recoil, pretty potent round, compares to a .30-30, SKS's can be had newly imported for under $200, the only hard part is to find one that's hunting accurate, you can usually return them if you're not satisfied though, or at least you can re-sell them for basically what you bought them for-not to mention they're fun)
Like I said, there's really no reason that you should need to buy a smaller rifle unless you're small for your age or are overly sensitive to recoil (which isn't bad, I've seen 40yr old 250# men that shoot .243's because they don't like recoil)...
My overall suggestion is either a .308 or .270 in a standard weight rifle, and mount a recoil pad, you'd be just fine with it.