So can you suggest a starting point in game programming for me? According to my research, C++ seems like a good language for game programming (correct me if I'm wrong). Should I begin learning C++? If yes, can you recommend a book for it? And if no, what do I program in?

You certainly cant go wrong learning C++, which is the standard programming language in the games industry. It will also introduce you to low-level concepts that you probably havent been exposed to in your previous development experience.

Game Maker isn't just about drag and drop.

If you actually aim on making a good 2d game you have to use the GML language (Game Maker Language). Which has similar syntax to java, c, c++.

You said you know Java so its going to be easy for you to get used to it and get started quickly.

I personally use Game Maker and I think its an awesome tool for making 2D games. (ONLY 2D GAMES!)

I have never used the Game Maker Drag&Drop tools cause I find them more difficult and limited from the actual scripting language.

It also supports multiplatform (andoid,iOS, windows, html ect.). At a given price of course...

If your aim is 2d game development then I think Game Maker is a good start.

Personally I started learning Game Maker from youtube videos of Shaun Spalding, When you get how things work you wont need any more help. Then it will be up to you. And of course there are game maker forums to help you out for more specific things,

Hope I helped.

Well, I'm not an authority source on the matter, but here's some suggestions about what I've been doing. It involves both some questionable or "Less-than-perfect" things as well as some solid stuff from well-known, established sources (like Stanford University, top developers like Will Wright, and more):

If you're into Java, then check out the youtube channel "TheChernoProject", it's a treasure trove (imo after never having found an equivalently educational game programming series from an actual top developer with years of experience). Particularly his game programming videos. Have in mind though, that you should probably couple this with some academical lectures like Stanford University's Lectures on Programming Methodology, as well as some books like "Effective Java" etc, because I'm noticing that TheCherno does a few things a bit cluttered or ineffective (by the standards of second-opinion professionals that I've talked to). Some pros have commented on him being a bit lackluster on commenting and structuring his code and certain other methodological things which I've heard is a major issue with coders, especially if you're applying for a job.

As Prof. Mehran Sahami (Stanford) alludes to, a great programmer can still be a horrendous software designer (and vice versa, apparently).

Also, you generally want to have a critical mindset regardless of what you learn in life, because this can prevent you from learning a lot of crap that you later need to unlearn. Intrinsic versus extrinsic learning, and all that good jazz.

For more conceptual stuff about game design etc, you might want to check up on Game Design with Will Wright and many more Youtube videos (and books).

Finally, never stop educating yourself. I've probably watched 50+ game design videos, read a few books (both on design and writing) and studied well over 500+ major game titles and now I just need to master Java so I can actually construct actual applications, which is ultimately the big bottleneck for many newbies, it seems. Then I'll move on to C++, most likely and later specialize in some specific field of game development.

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Finally, never stop educating yourself.

Best advice!