I am guessing you would rather have a sit-on-top for your 13 yo. Much safer IMO than a sit-in model. You can go to Pensacola Kayak & Sail and check out the 10 and 12 foot models - anything bigger may be too much boat. harder to handle, heavier to toteand the bigger boats are designed to carry heavier loads - a child may sit real high out of the water on a longer, bigger kayak. Take a look at the Tarpon 100 or 120 or the Ocean Kayak Caper, Scrambler. The Mainstream Kingfish mayalso work well - it is usually available at around $400-ish at Academy.Buy a decent seat and paddle - otherwise, the experience will not be as fun. Expect to pay $75-$100 for a good seat and $75 for a good paddle. Carlisle makes a nice light paddle with yellow or orange blades for $75 at Academy.
Academy has the Ocean Kayak Speck Edition on sale for $299.00.... I have one and it is a good Kayak. You will have to buy a OK seat from Academy for $60-$70.00. And you can rig it up anyway you would like.