I like to cut them out of 1/4" thick MDF. The MDF is easy to paint and cuts fast. Just make sure you wear your dust mask when cutting MDF. The dust from MDF is not very good to get in your lungs. The MDF can be purchased in any of your big box home improvement stores. You can buy the easy to handle 2' X 4' sheets. It's much cheaper than wood and you will usually be painting this project so why not use the cheaper material.
The edge of MDF is porous and does not accept paint very well. To help this I make a slurry of water and wood glue. I use a paint brush and paint the edges with the mixture. After it dries it accepts the paint much better.
It's often best to just leave them unfinished and let the parents paint the color they like.
One thing that is tricky is to hang the letters on the wall. You want them secure because the parents will usually hang them over the crib on the wall. Heavy duty double stick tape works pretty good if you buy the good stuff.