Internet Fuction

Hey guys, I just wanted to get an input on how LOL internet system and how my frame rate, and processor effect how well my computer runs. Right now I have a mediocre windows 10 laptop I play on and I plan on paying well over 800 bucks to buy a new one to fit my gameplay dreams. However, I wanted to fully understand what properties I needed to prioritize when I choose this laptop. This will be the laptop I game on and the one I will play against top guys hopefully later on down the road. So I don't want my ping or lag spikes to be the reason I fail smile baron or lose a last hit battle top lanes ya know? Any input??