Hi Marek.
Welcome to the Go Community.
_ First of all, since you just learnt the rules of the game you should first gain some experience 'quickly'.
'Quickly' means that you should play as many games as possible on the shortest amount of time, without thinking more than a few seconds each move. Why? because when you don't have any experience, you don't know what to think about and end up thinking about EVERY possible moves like a chess program except you're just a human and since you can play almost everywhere on a Go board there are too many possibilities for you to think about... AT FIRST.
The thing is, when you have some experience, you think about just a few moves that 'seem' worth thinking. And you can only do that with experience or knowledge (which is a kind of 'borrowed' experience). But before you read any book, I think you should play a hundred games or so before in order for the reading not to be too abstract.
There's a Go Proverb: 'Lose Your First 50 Games As Quickly As Possible'. You can read more about it at Sensei's Library (which has plenty of studying materials by the way).
_ Second: Don't play your first games on a 19x19 Go board but on a smaller one like 9x9. Why? Because a game on 19x19 is very very long and since you'll make mistakes almost EVERY moves, you won't learn anything from them at the end because they were too many of them. On the other hand, when you play on a small board, your mistakes are fewer and become more obvious and understandable so you can benefit from them being exposed by your opponent and try not to repeat them next time. Which leads to my third point:
_ Play against stronger opponents who will punish your every mistakes properly. The thing is, when you play a beginner like you, you can win regardless of your mistakes which will incite you to repeat them again and again. Whereas if your mistake is punished once, twice or three times in a row, you'll think: 'Wow! This really was a bad play! I'll never do it again'.
Because Go is a game where the winner is usually the one who made the less mistakes (of course some mistakes are bigger than other, but regardless, I think it's a good rule of thumb).
Now, since it can be hard to find a stronger opponent willing to play on a small board against you, you're lucky because here is a very good FREE Go playing program: Leela lite. You can play 'rated games' on a 9x9 board against the program which is incredibly strong for a beginner, but you begin with handicap stones (9?) which give you a very big advantage. As you beat the computer your rank will gradually improve and you'll have less and less handicap stones so it'll be harder and harder to play. With this you can learn how to play proper tactics before approaching strategy on a bigger board size.
_ While gaining experience by playing games is fun, you can also do so by solving Go problems. At this stage Life and Death problems suited for your level would be the more relevant choice. You can find them at GoChild website organized by strength and subject. It's very different than play games but since you said you wanted 'food for brain' this could be the perfect place for you. Give it a try anyway.
_ After playing a hundred games or so with Leela, which would have given you some experience and cleared the biggest beginner's mistakes from your play, then you should try playing on a big board for fun on such Go server as KGS and OGS, but still quick games at first to gain some experience on this scale before beginning to really 'think'.
_ Finally, once you have some tactical and strategical experience gained on your own, I think the time will be ripe for you to start to read theoretical and exercise books and such. My first recommendation would be the first volume of Cho Hun-hyeon's Lectures on Go Techniques. I read many many Go books but this one really increased my level by a fair amount (from around 18 kyu to something like 11 kyu if I remember correctly) and is like learning the ABC: first letters, then syllables, then words (the sentences would be on the sequel). After that there are many other books that will be useful depending on what specific area of your play you'll want to work on, but no need to rush: we'll talk about that when you're ready for it. 
Anyway, those would be my recommendations, and I hope it'll be useful to you.
Good luck.
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