Board Game Arena

As I posted in an earlier post, I'm on the hunt for a public domain game that I can use to get my feet wet as a BGA developer. Would it be okay to make a game that has licensed variants, but the game mechanics are public domain? The example I'm thinking of is Rummikub/Rummy-O/Deluxe Rummy etc. I was wondering if I made it and gave it non-trademarked name like "Tile Rummy" or something like that if that would be okay to make? I know I would need to make all of the graphics and artwork myself, but if it's okay to do, I thought it would make a nice, fairly simple starter project for me.

Sorry I'm asking so many dumb noob questions!

As I understand it, you can do any game you like, even one someone else has done, it just won't make it to the public site without publisher approval.
That shouldn't stop you from picking a game you understand well and learning the platform with it.