Looks like the first thing to do is rip out that old wood on the transom and replace it with some new Plywood sealed with at least 3 coats of Spar urethane. While you have it off you can sand or wire wheel all the metal under it, along with the rest of the boat, clean it and check for leaks.
Fill in any holes or leaks with JB weld, paint/seal up the transom and install the new wood.
I noticed the wood on the transom doesn't quite mate up to the sides of the boat (specifically the left side of the pic). When you build the new one I would make it fit nice and tight, it will add some structural rigidity to the back of the boat to help support weight and whatever motor you put on, not to mention it will just look more professional.
If the boat doesn't leak I would just prime and paint it. Some guys are putting Steel Flex, durabak, lineX, and other like products on the bottoms to help with sealing rivets, adding strength and durability. Its all up to you.
There are a lot of guys on here that have some serious skill and knowledge about this stuff. Way more than I could ever hope to have.
Take your time, have fun with it, and keep us posted on your progress.