So many ways to achieve this!
I would recommend going through some tutorials because you will undoubtably get stuck on many things.
I like to dive into things as well though, so to answer your question search the forums for how to make sprite buttons (look in the mod Kyatrics signature for a wealth of great information for newbies), once you click the (character) sprite button you can then set that character to a checkpoint - at the beginning of your stage.
Your character selection screen could be a totally new "layout", or simply a new "layer" that will appear on top of the game itself.
If this seems like too much, go through the tutes - in a couple of weeks you will be amazed how much you have progressed.