hi,
i was not study formally at a game college, just an IT app.worker for company.
now, i am also learning game development, and this is my 2nd & half years (but still not selling from this, yet 
).
start from 1 year ago, i try focus my study from 2 of game-programming ebook(Dawson's or Mitchell's).
thanks to the authors, for their kindness to share.
a game-programming book, sometime used 1/2 or 2/3 finished work(of a game) for their tutorial, build from chapter 1 until the last.
after i finish read, all chapter, i really don't have idea about what to be created first, at that time.
as starting point, i possibly do:
* create my own basic code struct, based on what i learned from the book.
* or, fix some mechanism to my own style (whatever things as you think proper/understandable for you, and should you have fun about it)
* use the game idea from the book, to create other similiar game, but of my own wish, my style.. 
by learn from other people which already experience in development until publish a game (big game, or mini game),
actually we speed-up ourself to be a game developer (artist, or programmer, or music composer, or maybe script/story writer, etc),
which is a person whose active in a game development.
-Do I need a game engine and wich is a good one for not just learning for wasting time?
** you can use anything tools, that easy for you to learn, and you like it. if don't, try to find any else.
i use c++, some peoples use c#, java, phyton, unity, etc.
perhaps not stick to long in finding the tool, since every time, every year, there are new tools coming, never end..
try focus on create & finish the game, not the tools.
except you're already start work at game studio with their operational standard tools, then maybe you will have to mastered it.
start your work by list your idea, features(simple and possible), goals, then start to code.
try-try hard to finish your work no matter how long it would take. always test, you're the first gamer to taste.
by doing that, you are experiencing a game development 
** if you choose to use 3D tools.
i'm not a grap.designer, honestly i find it difficult..
but still, very possible to learn. not easy, but once you know the basic, you'll (automatically) be dragged-in to
explore more to achieve your idea. so, find the specific book.
to learn, is one of the valuable parts of a work.
-How do I learn a programming language well? With a book? Internet tutorials? And is a big book "enough"? I think there is much experience I need too, but I dont think a book is enough, but there is mostly just one book, and how should I know, what book to use next, for a good connection to my knowledge I got from the other book?
** one book at a time, then create a thing or two.
implement it, taste it.. finally, ask other(your friend) to play, test it, is that tasty ?
** right after you implement a game, from your study from a book,
possibly you will notice how much you've grown, what is your strength point, and where is your most passion of game dev. focus area.
which is, that will lead you for another learning path essential to you. have to walk it, experienced it.
the other part of the development, of course, are to fixing or put some add-on (features, stage, objects, movement, etc).
development will never stop, even continue at the other next project/game.
so, based on your study from others, start craft your own method,
in purpose to create your own game, your style, and then let other people to taste it..
