At $200 you're looking at Chromebooks, but you'll need something with a Windows OS so the Ideapad 100S is probably your only real choice short of you getting an insane deal on parts and doing it yourself or going the refurb route.
I have an Ideapad 100S and it's not a gaming PC, even games like Hearthstone and FTL while they run need to be at low settings. Still, that's probably your most realistic choice with your budget. I would strongly consider saving some more money.