I made my game's protoype in python-pygame, but now I want to transistion to C++ and make it again from scratch. I am steadily learning C++ now and I want to start tinkering with my game as I study. But I am not sure of what starting point should I use.

What I mean with "starting point"? - Should I start with a graphics library/framework or is there a premade game creation utility software that suits my needs.

My game is going to be a space empire grand strategy game. It will encompass entire galazy as a map. Smallest interactable units of "real-estate" are going to be star-clusters. These star-clusters represent hundreds or even thousands of stars or even hundreds of thousands of stars. Star-clusters are going to be most of the graphics (plus some triangle shaped sprites for fleets). I would prefer if implementing graphics didn't take too much computing power as a lot will be required to calculate all the AI agents in the gameworld. It is going to work sort of like Europa Universalis IV or CK II.

So, what could be the best "starting point" for my graphical needs.

I stumbeled upon SDL 2.0, it seems rather promising. I might use that.

Do you have all the game logic (without the graphics) already running and debugged, at least in a "bare bones" fashion? If not, and you're still in the process of learning C++, you may be better off adding graphics later. You might want to even start out with a console app, to make sure you've got the basis just as you want it, in a platform-independent way.

How you handle graphics is going to be specific to APIs and platforms and should be what you add to a working concept, rather than where you start.

What do you mean with "game logic" - I am not familiar with the common game developer's lingo yet.

I don't really want to dedicate too much work to graphics. I just want to get the basic graphical representation out of the way, so that I can focus on the mechanics and rules of the game,

so that I can focus on the mechanics and rules of the game,

That's what I intended for "game logic." I'm not sure how you can know what graphics you'll need until you know how the game is to be played. That is, have you decided what you want the user to "see?" Menus? Maps of territories? Inventory? Opponents or friendlies?

That being said, SDL may serve your purpose. And, certainly, in the learning process, if you want to try your hand at graphics just to see what it's about, experience is often the best teacher.

A rough version has been done in pygame/python and I have pondered about the interlying systems intensively. I can say that at least I require a representation of the "real-estate" as that is going to be the base of the game and everything is built upon them. With the star-clusters visible and interactable on basic level I could think of more advanced mechanics and rules.

At first I am not going to include many features for user, perhaps only a developer environment of sorts. I am interested to flesh out the AI and AI-AI interaction and only then add to user the possiblity to do something that AI can already do.