Budget Laptop for Smaller Games

I'm looking for a laptop that can run small games (Minecraft, Starbound, Terraria, Pixel Piracy, etc.) at smooth rates. The main problem here is that Starbound and Terraria may not be demanding, but eventually will have lag due to high particle amounts. For example, the portal to the Ruin made the laptop lag in Starbound, but nothing else can. And, let's face it, Minecraft, while pixelated and blocky, is still hard to run well. The only way for me to run it at ~60fps is to tweak with OptiFine and use a 32x resource pack. I also frequently use Google Chrome, and I hate having slowness (although I know it is impossible to completely remove it) while surfing the web. The problem here is that I am not old enough to work, therefore I barely have any money, and the person whose laptop I'm currently using moves out in January, 2018. Can somebody tech-savvy build me a cheap laptop to run these games perfectly smooth?

 

How much budget that you have? Perhaps 300-dollars laptop would be able to run all of that games fine. Just make sure to choose one with APU or even GPU included.

 

Id like to go less than $500, and lower is better as long as I can play with little to no lag, and mods (CFM, Better Than Bunnies, but not things like Crazy Craft.) I'm willing to spend more if I can get my hands on the money, but it depends on how much I can earn/receive.