Welcome to the SP2 club!
You'll also enjoy something you can't with your S2, sadly, Windows 10 when it comes out
It will be officially supported.
The problem with Intel integrated graphics is the lack of full DirectX and OpenGL support, despite Intel claims. You'll encounter with games that works fine.. other would be "fine" (low fps), but you'll encounter games that will crash at some point where the only fix is to drop the visuals to avoid the DirectX or OpenGL call. Some games won't even start and crash immediately. Very sad. I wish that Microsoft join with Nvidia and bring the Tegra X1 GPU as stand alone chip to the Surface Pro 4. That GPU is more powerful than Intel best offering, and requires no fan or heatsink. Even, if the GPU is identical in performance to Intel, the simple fact that it would truly fully support DirectX and OpenGL, not to mention DirectCompute, CUDA, and OpenCL, would be a huge plus.
You don't need 2000$ for a gaming computer. That is overkill.
You can build a desktop with a sweet Nvidia GTX 960, Core i5, solid case, 80 Plus Gold certified power supply, and Noctua fans (last 2 for quietness), for well under 1500$.
Very quickly I built you from Newegg.com:
->
Case: Fractal Design Define R5
-> SSD: Samsung 850 EVO - 250GB
-> HDD: Western Digital 1TB Black 7200RPM HDD
-> GPU: Nvidia GeForce GTX 660
-> CPU: Intel Core i5-4690K (you can drop the price if you don't get the overclock-able model)
-> Motherboard: GIGABYTE GA-Z97X-SLI
-> CPU Heatsink: Noctua NH-U12P
-> PSU: Corsair HX 650
-> RAM: G.SKILL 8GB DDR3 1600MHz
Total: $1,139.91 U.S at Newegg, and I have not looked for prices at all. So you can drop the price further
Add ~100$ for Windows OEM license
Anyway, something to look at, this is not a forum related to building computers. If you join one, people will help you in finding you the right parts, best for your money (giving you more savings), and lowest price (even more savings), and even help you build your system (I think NewEgg offers a service for like 50$ and they can build it for you if you don't want to do it).
Let me know if you want a suggestion for a forum that will help you and are nice, and I'll PM you one.
Anyway,
You may be interested in this software for your Surface Pro 2:
http://www.surfaceforums.net/threads/surface-tweak-tool-for-surface-pro-2-release.8219/
Hope this helps. If you have any questions just ask.
The way I make my Surface Pro 2 an extension of my desktop, is that I use OneDrive. Both systems runs Windows 8 as well for account sync as well.