i think somewhere here on gamedev there's a list of most of the game engines out there, or it may be on wikipediaYou might be thinking of DevMaster's "DevDB".
actually i was thinking of this one....
http://en.wikipedia.org/wiki/List_of_game_engines
and this one....
http://freegamedev.net/wiki/index.php/Free,_cross-platform,_real-time_3D_engines
In my opinion, it depends.
If you want the educational approach, I would create the sidescroller engine, battle engine, etc. Learning how tiles moves, how turns switch back and forth. For this approach, plan a mini version of the engine and see how everything plays out.
If you want the quick approach, just find an existing one. Then again, you will need to learn how the engine works before you even make progress with your game...this approach might be slower depending on how quick you learn the engine.
But since you are just starting out, I am not sure if you have a full grasp on graphics ie: how to draw them on the screen, basic game features: how to create a program flow from menu transition to gameplay, basic animation, collision detection. If you do not, start with this. That way you have the skill to build the engine.
