I would check out the Mission Bows that are made by Mathews....the 2 I would check out are the Mission Craze and the Mission Riot.The "Craze" starts out at around $300.00-$325.00 and can be adjusted to several different draw lengths and goes from around 17-20lbs up to 70lb draw weight,it is a short 28 inches axle to axle and it a great Bow You can grow in to.
The Mission Riot is another great adjustable Bow and starts out in the $400.00 dollar Range.
I bought the Mission "Craze" for my youngest Daughter (15 years old) to start out with and if she doesn't stay with it I'm going to have it adjusted to fit my larger size and Hunt Whitetails with it this Fall.I think its pretty cool that I can shoot the very same Bow as my Daughter and have it set to fit me,an older/larger sized Hunter!
Used Bows can have issues and need to be checked out by a good reliable Archery Shop to see if it needs a new string,check the cams and limbs for cracks and have it adjusted to fit a different size Shooter...re-sale on a used Bow are pretty low,with all the different new and better bows an older used Bow is pretty hard to get rid of and they go pretty cheap.