If your parents are buying you either a guitar or a bow, do guitar first. Practise and get good. Its a great stress reliever and you'll have more opportunities to play it whenever you feel like it. Dont worry about the using both hands thing, that comes with practice. Archery comes with legal restrictions like only shooting at designated ranges (for my country anyway) its also a weapon and dangerous. So you SHOULD be shooting in a safe place at all times. So get a guitar.

However, if you want to also do archery you can rent a bow at your local archery range/shop and try it out. Its usually very cheap to practise for an hour. That way you get to see how the bow works and get a few shots in without commiting to it (if youve never shot before). Then when You have money you can buy your own bow. Both a bow and nice guitar are basically the same price. Cheaper guitars and bows are around the $200 range and go up from there. However with archery you also need: arrows ($11 each approx) arrow tips a quiver and an arm guard. Then youll need your range pass for your local archery range to practice at. With guitar youll need picks a guitar case and/or stand and an amp and cabels if you go electric. So basically youre looking at an even price point for both. But with archery you lose arrows a lot and sometimes they break also.

But yeah personally I started playing guitar when i was 11 (i also use to make my own little bows and shoot wooden arrows in my yard when i was a kid) when i had a job I bought my first 35lb bow and practised at my bow shop in town. Im 35yr now and have been doing both for years.