*facepalm*
There is a
drop-down menu in the ship editor where you can choose the class of each individual placed ship. Double click on the Player, click on the drop down "ship type" thingy in the upper-left portion of the window, and choose your desired ship class.

The "player ship" checkbox has nothing to do with this. But if you're curious, when FREDing a multiplayer mission, you have multiple player ships, yes? To make a mission a multiplayer mission, go to IIRC mission-specs, then somewhere there, there will be a circle with "multiplayer" beside it. Choose that. Now, you can check and uncheck the "player ship" checkbox in the ship editor to your heart's content.

EDIT: If I could run FRED on this compy and take a snapshot of the stuff for you, I would. But I don't have FRED here.
EDIT2: BTW, you do know that you can choose which type of ship you want to pilot from within the game itself, right?