Unity or Unreal Engine 4 get my vote...
(note that UDK is legacy now, UE4 is pretty much better on all fronts, coupled with an attractive price point and low royalities, so there really is no point conidering UDK for a new project anymore).
Both very capable engines, with lots of documentation and large user communities. You should be able to do pretty much everything you can achieve as a sole dev in these engines, once you get to grasp with the engines editor and have some expierience with programming. You will need either an artist, some artistic talent and time for that, or money to spend on art though, if you want to do more than just very basic graphics (which will be very much fine for prototyping or just learning though).
I would also stay away from CryEngine. While certainly a very powerful engine, the Editor looked pretty dated and hard to use the last time I tried, and with a smaller user community you will have a harder time getting the hang of things anyway. And then there is not much point going for that engine anyway when Unity and Unreal 4 can do pretty much everything you could strive for.
In the end, just pick an engine and stick with it until you are able to use it. At least between Unity and Unreal, you most probably cannot choose wrong. If you are already used to Unity, stick with it. There really is little reason to switch to a different engine at your stage.
And I would also stress sethhopes point: learn to program. Best before you even start using engines. Failing that, make sure you set aside some time to learn the basics while playing around in the engine.
Even if you do not want to become the most hardcore graphics or gameplay programmer in the world, without some programming skills, you will not get too far in an engine.
About the hardware:
Be aware that you pay a hefty premium for laptop hardware, especially if you already have the screen and keyboard/mouse lying around and don't need to buy that new for the desktop equivalent. You will pay at least 50% more for something that is most probably giving you slower performance than the similar price tier in desktop hardware.
If you are still convinced you need a laptop, next you need to think about how you will use it. From what you describe, you don't need an ultraportable laptop. Scratch off all that ultrabooks, macbooks airs and hybrids. Why? They are using the powersaving laptop class hardware, which is quite limited in its performance (for Intel for example you will only get dual cores, no quad cores, clocked to a much lower frequency), and 90% of the time without a dedicated graphics card.
The good news is for you: the less portable laptops, or desktop replacement laptops are generally cheaper. You could look for a decent 15" or 17" laptop, and as long as you don't aim for gamer-class laptops, you could get such a machine for around 750-1500$, depending on your exact performance requirements.
Of course, don't expect a top of the line mobile GPU for that, or the fastest i7 ever, but its about the sum you need to spend to get a decent machine. a rather slow one or with many other compomises made on the lower end (bad screen, bad keyboard, flimsy build, ugly design....), or a rather good one with middling specs for a powerful desktop replacement laptop at the higher end. More than that you will only need for high end graphics development, or 3D modelling. On the other hand, if you even try to open an engine editor on a slow Core M with a middling Intel iGPU onboard, your expierience will be rather bad, as both the CPU and GPU will be competly running at their limits while still giving you low performance most probably.
About the choice of OS: Linux isn't a very good choice for game dev for a multitude of reasons... driver support, engine editor support, and so on. Also, your future users will mostly NOT use linux. That might change with Steam OS, but that is still some time away until it really takes off.
MacOS is pretty much mandatory if you want to target iOS and MacOS. I guess there are ways around that, but Apples stance more or less is that you should use a Mac to build for their OSes... So if you target i-devices, yes, you will need a Mac. For MacOS, IDK... I wouldn't even target that until you have your Windows build ready and tested...
Because the 1000 pound gorilla in the game dev world is still Windows. There is no way around it, if you target normal PCs regardless of the OS, around 90% of your audience will use Windows (don't know what the current stats are, could be closer to 85%, but that is beside the point)... under 2% of your potential user base is using linux. Now, this stats are usually coming from a service like steam, which will introduce all kind of bias to it (maybe windows users are just more inclined to use steam because most steam games are built for windows), but the ranking is pretty much spot on when it comes to PC Installbases worldwide. Windows is in the lead, MacOS has a much smaller base, Linux is third.
Now, this led to the situation that even tools originally built for MacOS (like Unity) or Linux quickly ported their tool to windows, while the other way round that might not necessarily be true. So on Windows, you get the full set of tools. then, DirectX might not be the best middleware ever, but it seems Microsoft is getting pretty active with further developments on this front, and DX is exclusively being developed for Windows (and XBOX).
You can build for Linux or Android without any problems on Windows (don't really know if there is a way to do that for iOS or MAcOS without owning a Mac though). And as most gamers are on Window, driver support for graphics cards are usually most up to date there.
So yes, my call would be: Go with MacOS for iOS specific development, go with Windows for everything else.
