Well, certainly setting the bar high. I am not one for anyone to say you shouldn't do that. If you have a goal then you can shoot for it. Thankfully there is also a bunch of open source engines out there that you might be able to get the code for that will help you along your path.

In many instances the engines are often specific to the game you are writing. This isn't a hard and fast rule. But to leverage something like FrostBite 3 to make an MMO would require a lot of changes to the way some of the networking stack is implemented. But that isn't to say that general engines, tweaking here and there can make any game you want. So it might be helpful to see some RTS samples. See how they work internally as a game to get an idea of what you will need to implement in an engine.

JavaScript is a good place to start for languages, it can lead nicely into Java, C# and then in to C++.

Engines, the best thing to help with this is interfaces and document models. But this I mean how will you write the game that to connects to the engine, how easy will the calls be to perform the draw things of that nature. Hide a lot of the plumbing behind good interfaces enables the game developers to concentrate more on the details of the game and not how they are going to get the thing working properly in the engine. So understanding the game engine architecture would help. Understand the basics of what is needed in an engine.

Graphics, Sound, Input, Network anything like that. Then dive into each of those deeper and deeper.

I hope this helps some. You have given yourself lofty goals if you are still learning the basics but stick to it and push yourself. It isn't impossible, but it will not be easy.

Having a "taste" of different languages is indeed an excellent idea.

I'd personally stay away from Java. It's just too verbose and HTML5 can do many, perhaps even most things Java excels at. The library is quite verbose and system integration is, in my opinion, still lacking.

However, no matter what you do, you will never be able to build an engine (in the sense of multi-game shared platform) without writing a few games first, possibly from different genres. Your resulting design would just not interact well with the gameplay constructs or the data flow involved.

So, next step in your path to engine design is: write an engine (in terms of logic for a game).

Earlier given advice by the others is perfectly valid.

Personally, if the aim is to make a game I would take the "make games, not engines" approach. This doesn't mean you won't make the engine though. Just start off with getting something on the screen, as in, make a basic 3D render engine (or 2D if that's your aim). From there on out, focus on what you need for your game (collisions, physics, sound, etc) and build that. Build it with re-usabilty in mind. Pretty much what EarthBanana said. :)

In the end, you will have a couple of building blocks that make up good start and basis of your engine and on top of that, you have your game.

You will find flaws in your systems, things you will want to do differently next time, make (stupid) errors and everything else wrong. But that's something one will always have, even the best still make mistakes, but on a different scale, so never let that be a motivation killer.

Just keep in mind that getting the game engine is a long term goal and that you should learn from making it, whatever way you choose of making it. It's best to look at it as an iterative process.

Good luck! :)

I started off with Basic back in the day and then I moved onto Turing and then in high school I learned Pascal. Once I got to university I picked up C/C++ and then I found that learning other languages was pretty easy like HTML, JavaScript, PHP, ASP etc. So if you want to be a coding guru, I highly recommend learning C++, it seems like other languages are much easier to learn after you have a good grasp of how C++ works.