This Brett Bros. Maple/Bamboo Wood Baseball Bat (MB110 Adult) would be a fine model to get a player at 13 years old for his first wood baseball bat. It is built of the maple and bamboo material to allow for better durability. As well, it will be pretty balanced in its feel which will help the transition, especially if he is moving from a lighter swinging bat.
Bats like the Brett Bros. Maple/Bamboo Wood Baseball Bat: MB110 Adult are not professionally approved since they are not made from one solid piece of wood (ash, birch, maple). With regards to a semi-pro league, hitters might be able to swing them if you check on the league rules.
The Brett Bros. Maple/Bamboo Wood Baseball Bat: MB110 Adult will have a length to weight ratio of -3. Thus a 31 inch model should weigh 28 ounces.