Traditionally, you would be baptized naked and then given a white robe. Babies are still taken care of this way.
For adults in our day and age, there seem to be various practices from place to place. For instance, in many places, one would wear swimming trunks and a t-shirt when being immersed, and then change into a white robe. However, in other places, one would be baptized in a white robe (with underclothing) and then change into a normal set of white clothing afterward.
It seems to me that most people are not going to wear a white robe to church for 8 or 40 days after baptism, so a white set of clothing would be fine for after the baptism. I have baptized people in a white robe and then had them wear normal white clothing afterward, and I have also had people baptized in regular non-white clothing and then put on white clothing afterward. I have not baptized someone naked or in regular clothes and then had them put on a white robe...seems to be a bit superfluous to me to have someone pay 75 or 100 dollars to buy a white robe they will wear for one service and never again. However, the robe is obviously what we use for infants and probably more traditional for adults, although the question I would like to know is what they had Muslims wear upon conversion to Orthodoxy during the Turkish rule (the rare times that happened). That might give some insight into how the ancient practice carried over into modern times.