Well Son
There are over fifteen calibers that have taken deer successfully, surprise to some, of which the .243 and .308 are two.
Of course we all have to start somewhere, and we all can't start at the same place. I started and dropped deer on the spot with a lil ol 35 Remington Marlin. Had a hard time moving to another, but never gave the .35 up. My start which nobody has to copy.
I'd first look to see how physically big you were and ask if you had any experience with recoil. Both calibers will work. Just practice and learn how to shoot it.
When a buyer selected a caliber, which I knew was successful, I'd say, "Son, you picked a great caliber." Even if I never used it. I knew it was successful, and used by somebody. And in the end, that's all that really counts.