To port to Android, you must use the Android SDK or LibGDX or similar library. LibGDX is specially made for porting to multiple platforms. Trying to port a PC version to the MAC is one thing...they are fairly similar systems...but moving a PC version to Android is completely different because you have to worry about touch screens and lots of other Android "stuff". If you want to port to Android, that is something you need to think about now because then you should use LibGDX. In my opinion, since this is your first project in Java(even though you have some prior experience with games) you probably shouldn't worry about being cross platform and just getting your game out there, in which case I would recommend Slick2D over anything else.
So I guess a library or sdk will do the graphics thing for me or at least make it easier? Also would you know if that could be implemented for android if a library is used or would that be library specific?
Slick2D makes the graphics easier and is less laggy than "vanilla" java graphics because Slick has hardware acceleration. Games made in slick are "state based"...your menu, game, game over screen, high score screen, etc. would be different states that have their own independent update and render loops. Slick has lots of cool lighting effects and fade transitions that can make your game look way more polished. (My one problem with Slick is that it has trouble playing MP3 files so you will have to use a separate library for you audio playback and processing)