One thing I've learned over the years of building my own PCs is never settle for less than you need/want because you'll only end up disappointed... no one wants to buy a new PC to run a recently released game on Medium graphics, yano?
As
@Noxot said, built-in graphics are basically a really bad idea if you're wanting to play something other than browser games or VERY light graphics games. They're good for being able to watch 4K TV series etc on, but for gaming... no.
What's your budget?
Also, small form factory is only something I'd use for something purely functional and less performance oriented. I used a small form factor for my home lab system to experience with different OS's and software, but that's because it's nice to just have it tucked out of the way.
With gaming especially, air flow is important and small form factors really lack in that area.
I am using
this case now and I love it. It comes with 3 fans stock(140mm air flow fans) but I'd replace them with static pressure fans and use 2 of the stock fans as exhaust fans in the top slots where the radiator can go.
Drivers really aren't an issue anymore. Personally I stick with NVIDIA because they typically perform better and have less problems than ATI/AMD stuff, and you get a control panel with it and you can just update drivers with a press of a button to download and then express installation. It's really straightforward.
As far as power consumption is concerned, PCs aren't that expensive to run really. More modern series of GPU's are also very good on power. I'd recommend the NVIDIA 10 series card, depending on your budget, even the 1060 is a great card for the money.
Oh and go for Intel!
TL;DR -- If you have to save for another 6-9 months to get what you want, do that. I've skimped and rushed it in the past and it's really, really demoralising.
If you need help picking parts just let me know.