You need to double your budget for a gaming laptop even for lower settings on newer gams.
Minecraft may be OK on lower settings without mods on a regular i5 system. i3 may be a bit too slow.
Either way, won't be for $300 unless you get a used system. For $300 you are looking at basic laptops that can browse the web and watch movies. A system to handle games even on low settings would be about $500, anything less you will wish you spent the extra money. Just look at craigslist and all of the cheap laptops people buy, keep for a month then realize it's too slow to do anythig with and sell for 1/2 the price. You don't often see fast new systems for sale, but a ton of low end stuff.
I'd think about a used system in your price range if you want to play games on it, a 2-3 yr old laptop that used to be $800 new is a lot better than a $300 new system. Just make sure you see it running without crashing for a bit, runnng a benchmark like 3DMark would be a good test.