Hi, I have 3 boys ages 4 and under and there are 2 ways you can go here. one is to transition him into a full size or toddler bed WAY before baby is born because you don't want him to make any changes after baby is born because he will associate you taking his crib away BECAUSE of the baby. He will also regress a little in different ways after baby is born so making a change right after will not be good because he needs stability and security then the most. He will feel replaced but not know that is exactly how he feels.
The other is to wait a while after the baby is born then transition him to a new bed. but it really does matter what size bed. Some people use just a matress so the won't fall off and some use a toddler or full size with guard rails.
I used a crib tent on my toddlers crib for a while and when I started transitioning them to a bed, they have the crib still in the bedroom and if they do not stay in the bed and they get out, then I tell them " you stay in your bed and if you get out, then you go back into your crib" Then, if they get out, I put them back in the crib and zip the tent... they sleep in the crib that night, then we repeat that until the child stays in the bed and goes to sleep. (my boys always wanted to run around the room and play and come out of the room so we used the crib to show them that if they did not stay in there beds they were not ready to sleep in the big boy bed. IT really worked quick)
Also, we made a huge deal about letting them help pick out the big boy bed and bed sheets... so they felt like it was a big deal and would transition easier.
Good luck... A. J