Acer Aspire E5-575-33BM for $350. 7th generation Core i3-7100u, Intel HD 620 graphics core, 1080p screen. Based on user reviews and official reviews, it seems to have pretty good battery life of 7 hours with average usage (no games). I am actually thinking about buying this myself to replace my aging Lenovo IdeaPad Y470 from 2011. But I am waiting to see if it will go on sale during Black Friday.
https://www.amazon.com/Acer-Aspire-i3-7100U-Windows-E5-575-33BM/dp/B01K1IO3QW
The link below has some benchmarks for the Intel HD 620. However, be aware that the benchmarks are from laptops using a Core i7-7500u (3.5GHz max), not a Core i3-7100u (2.4GHz). The more CPU dependent the game is larger the potential performance difference between...