Start with pong, go to space invaders, maybe a maze game. From there, you can work on adding 3-d and then you will have the basics.
Well, technically, any codebase that allows creation of game content is an engine in itself.
The difference usually lies in the approach. Those making an engine exclusively focus on making it generic enough to allow multiple implementations; Those focusing on a game, on the other hand, develop features that the game needs, regardless of reusability.
So yeah, for starters, I’d focus into making the game first, and then for future projects focus on maybe expanding the engine that’ll come out of it.
(Mind you, all this advice is great, but I at least tend to be an idiot and ignore it. My current project is bogged down by my obsession to try and make everything as generic as possible, so maybe read this as “don’t make the mistakes I’m making” advice)
I’m surprised nobody mentioned Project Euler yet: http://projecteuler.net/
That website gives you a bunch of problems to solve, and you submit programs that solve them. You compete for points by solving harder problems.
Sounds like a Dad telling his son about women 
Now you say it. Still apply from game project, multiply the screw around step ;D
From a fellow java noob, here’s a website that’s got a bunch of basic exercises to learn and get good with stuff.
http://www3.ntu.edu.sg/home/ehchua/programming/java/J2a_BasicsExercises.html
I’ve only been learning java for about a week, but that website’s helped out a lot so far. I just made a number-guessing game(it’s one of the exercises) without having to look at any references or anything, which is a pretty good feeling.