Hi,
I would like to get started slowly and I was thinking about getting started with a game of checkers, even though the logic behind the computer playing the user maybe a little complicated, but I’m more worry about the graphics and getting the feel for UE4 than anything else.
If you’re more worried about graphics then try and join someone else for some project where they can program. Then you’re not wasting your time. If not that then look up tutorials for individual things you need or related things. Then go from there
Checkers should be a very easy game to build in UE4 (other than the AI, as you have noted), either in 3D or in 2D.
As far as AI goes, you should do some reading about the Minimax decision theory ( Minimax - Wikipedia ), this theory was used in the Deep Blue computer. The Deep Blue was built by IBM, and beat the world champion in a chess match.
Obviously there are many other AI theories for problem solving, and you will need to pick some method, or create your own, but for more difficult AI you should pick a theory that is effective.
Realistically you would not create your own AI. AI for games like chess and checkers are the realm of dedicated solvers, and are well outside the scope of individuals who don’t want to go deep into the rabbit hole with a complex piece of software. Most solvers (and all the good ones) actually work by having a database of all reasonable available moves and querying them as quickly as possible - less of an exercise in AI and more of an exercise in extreme database management.
I don’t think you would use matinee to move the checkers.
Agreed, that sounds kind of strange :\
If you just want to make something simple, I recommend a basic arcade game like Space Invader.
Why not try noughts-and-crosses? (That’s tic-tac-toe for most of you. 
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