Java is fine, but I would prefer to stick with C family (with some Lua scripting as additional option) if it's possible.
I want to begin with simple task, as you said (although it's not that simple to me:) and will add more complexity on the way.
Basically what I want is a grid of cells (each cell have a dot in the middle and a two states: 1-marked by user 2-free) then according to the cell state, if it's marked, then cell's neighbors states also checked and finally marked cell's dots connected and the resulted polygon filled with some color.
I want to grasp how it's should be done, language and framework agnostic?
1. Draw the grid, by drawing lines.
2. Draw a cycle in the middle of each cell
3. Player input event handler, player mark a cell, touch at position (x,y) which cell is selected?
4. Check neighbors cells states
5. Connect cells and fill polygon