IMO, the safest way to go, and besides, a skill that is demanded in quite a number of companies today is learning Unity. That thing also export to a number of platforms (mobile, html5, flash, pc, etc)
Probably easier is gamemaker, and can make your entrance smoother and pleasant. Plus, I do know several successful solid games done with it. Still, in the opinion of a freaking coding genius -a friend of mine, with tones of titles developed in his belt- for big projects it "might" be a problem. IMO, to start and so to keep the enthusiasm, is nice and fine.
What I would do if at my forties would have been beaten by the bug of making myself a game (am not, too old, little time... if anything, to do the graphic side of an indie game, never the coding) , I mean, if I were again 20, I'd probably now, BY ALL MEANS, would pick some engine which uses Python as the scripting language. A coding language extensively used by the Google company and so many others, providing lots of works in IT. Even more, there are some engines based in C#, C++ or even yet just C. Those would serve you to actually learn a language that helps you build as well a professional profile: In the future you would easily move to learn some bits to do as well database projects or any other app related stuff. That'd be, IMO, the really clever move. Sadly one doesn't happen to "know" this stuff in time...
I gotta say I do LOVE Python, even while I only know the basics, have just programmed parsers and other file and text handling applications to be able to make my own "dynamic" web sites, and even for very specific needs (meaning i have not programmed the next Dreamweaver, lol) and I gotta say is simple, useful, and practical. using that with the special scripting adaptation with some of the several existing game engines that are using it as the scripting language, could be a great idea.
It depends on your focus. if you really want/think you are capable (meaning, are decided, are patient and a very hard worker) of pulling a basic game (yeh, like Pong or invaders, go easy first), and then another and so till you learn to make a little more advanced, yet simple one, as a start in your "game catalogue" , but with the main plan of selling and distributing it my best advice woul dbe go Unity. if you are just wanting to make a game, but, like me, consider the enormous advantage of at the same time learn a programming language that is widely required in companies of all kinds, then go with any reasonably well known and established game engine that uses Python, C# or Java. Not necessarily in this order. I'm more fond of the first two, specially Python, Somehow I have never been much sure about java, tho is tremendously demanded in companies for non game related applications.My friend would fully hate me for saying this, he's a java genius....And have made tons of java based games. (and many actionscript ones (the language created for Flash))
If you just want to make games as a hobby, not huge ambitions, just to have fun, not a super huge implication as you have other more important duties and interests in life, then I'd say: Game Maker and Adventure game Studio (lol, I was in AGS forums like a decade or more ago, was even famous there...with another nick, of course) would fit best here, imo.
Unreal is THE BEST engine of all mentioned here. I am just wary of the licensing, (not just the 5%, some other small letter there which I didn't love...) and not sure is that easy for a newcomer as it is GameMaker or, even more the AGS.
One thing about adventure games, though.... They require TONS of graphics. As the art guy, I can tell you i tend to run like heck from adventure games, unless is done very cleverly, usually with pixel art, and reusing a lot the material by doing maps using tiles or whatever other reusable/recycling method. Doing 60 backgrounds in raw, is like 60 illustrations... i work mostly as illustrator lately, and i can tell, you that's not only time consuming, is... EXPENSIVE... well, as a result of the time factor and that we had some long years of training , is not so often that people get the fully professional level in that, so the cost of that can be quite expensive. Luckily, illustrations and works in pixel art style tend to be a lot cheaper. (which is sad -am also a pixel artist- but is somehow established so...)
Also, if you go that other route: A game engine which bases on a well known coding language so to reuse that knowledge in a future career in IT (or just to make some side money producing some app/utility) be careful in seeing the difference between a fully ended game engine from one in the works : It might never get ended, and rarely you would have the engine programming knowledge to complete it yourself. Also between a game engine and just a renderer or game library. Nowadays might not be so, but in its days, things like Irlicht Engine (scripting was c++, I think) or OGRE (C#, but not sure right now) were just renderers. You could build a game with them, but during many years you needed as well to code a sound system and etc, etc. That surely has changed, though, just be careful on what you choose.
Also, to what can it export. Mobile market is super over crowded right, Still, is an option. very hard to make money there, though. Consoles, too dificult to get the permissions and expensive licenses necessary in most consoles. Some are a bit more indie friendly than others, though, ideally, the best way to go is an engine that exports to several platforms. In that, I think Unity is one of the best choices, if not the best. But is not free, and indeed, is quite expensive.
All in all, if i were you I'd be thinking, if you are in a very initial moment, mostly in Game Maker and even maybe AGS. Butsurely as well giving it a good go to an engine that uses Python as an scripting language. IMO going into a coding language (even while used just as scripting for the game) like C#, C++ or even Java, that might too hard right now. Well, even Python, but imo, is by far the easiest of the bunch, and quite used, too. And helps in learning the programming methodology, although is quite different, of course.
Do some games in Game Maker, you'll realize the GML, its scripting language will be needed once you get into much more complex projects, and go anyway this route for 2D , tiles and sprites based games. Pixel art, that is. Which is surely the best aproach for now. I'm not up to date about that engine improvements, but would be really important , even if you need to purchase it (is very cheap) , that it counts with html 5 and flash export. This will allow you to do web games. And Flash is NOT dead, despite what everybody says... Is no more a platform to earn solid money -and I know as I worked with a friend for a year and some, and was even easy to get a company purchasing the game, or nice revenue from ads- There's still a window of oportunity for a GREAT game to make money in Flash. but if anything, what is replacing Flash is HMTL 5, so an engine exporting to both is a total winner. Yet though, with the triumph of mobile in gaming, way fewer people play web games these days. there are still, though.
Last advice: Go with the trend. Go with an engine that has massive user installed base, as is what is gonna survive. For this reason, i would only consider Game Maker and/or Unity. A game engine based on Python still is a great idea, because learning the language is already a huge advantage by its own.
With any game engine/environment, though, you will learn the procedure of making a game, that's for sure. And will get used to scripting even if the languages might differ a lot. But you will somehow get the mechanic of it. Later on in game companies, lots of programmers are actually "making" the game in scripting languages, like one of their own, or things like LUA, C#, Python or Java. Because is how things have evolved. games are not anymore hard coded in C++ or C. That's usually the game engine, and there are game engine only coders, too, but that's another story, and quite a harder one, too.
if thinking of this as a way to earn a salary in a funny and relaxed way, forget it... Is hard as heck. I moved during a decade at the end towards graphic design and ad agencies for a reason. And that considering this other world is considering stressful per se, lol. IMHO, learning programming for applications, like Java, C# or Python is a very solid way to at least have something solid to get a job later, and a more stable one... We game workers are often needing to consider life as nomads... As game projects and full companies get born and die frequently, usually is per project. If I had kids I would never recommend any career related to games. For a hobby only , of course! Is super fun and creative (and even painful as a hobby, though)
I know the game making world looks very attractive but is better to be aware that is a hard world to survive in.(if plan on considering it your profesion)
Sorry the typos, typing super fast, wanted to cram a lot of info and am out of time to fix the ton of typos...
EDIT: Indeed, for the sake of a job in something related to coding, imho learning html5, javascript, (and there are already great games created just with these and javascript game engines ! ) , and PHP, gives you a ton of jobs... at least, today. As things change so fast that might get deprecated at any time and moment... But for now, that profile is hugely searched for. Programming for the web and web applications (as not all that is for internet) . And once learnt all that, go for Ruby and Python, hehe.