I am thinking about getting a Yamaha yz 125 and I am only 5'3 is this the right size for someone of my height?

A person your height will find the bike a bit on the tall side especially since you are talking the yz as they were the taller of the known brand 2 stroke 125cc bikes. The suspension can be adjusted to make the bike lower and trimming the foam seat also lowers the bike. If racing you would need starting blocks.