Tee Ball Bats
Most T-ball leagues will require player to have their own bat, so it is generally recommended that parents buy one for their own child. Tee-ball bats are generally very moderately priced and will run in the $10 - $30 range for the most part. Of course you can go higher, but this range is just right for a beginner. After all, T-ball players are learning the mechanics, so getting a high-end piece of equipment is a bit early.
Finding the right sized bat for your child is actually much easier than you think. Have your child pick out a bat they like and have them hold the bat in their dominate hand (the right hand for right handed batters and the left hand for left handed batters) with the arm and bat fully extended and parallel to the ground. Have the child hold this position for 30 seconds. You will know that you have found the correct weight when your child can hold the position for 30 seconds without the arm sagging and without the bat losing its parallel position with the ground.
Coaches should advise parents about their league's rules to determine if there are any restrictions on using only tee-ball bats. Some national and local league rules only allow tee-ball bats while other leagues have no restrictions. Youth league bats are a bit longer and heavier than tee-ball bats and these bats are usually intended for older children in tee-ball or in coach pitch levels.