MBP 2016 Monitor Help | Mac

Looking for a new monitor for my 2016 MBP with 2 Thunderbolt 3/USB C ports. Ideally I would like to use one of the ports for charging and one of the ports to power an adapter that supports a display and my wireless Logitech G613 and G602 peripherals. As this is my first monitor purchase I am completely dumbfounded on what to look for.

I will be using my MBP/monitor for gaming (CSGO, LoL, etc.), School and productivity, and a lot of video/movie watching.

I have around around a $350 budget for a display and a dongle with a display port (DP, HDMI, etc) and at least 2 USB ports (Gigabit ethernet would be a bonus)

I am very new to the whole monitor game and the specs for my laptop can be found here: MacBook Pro 2016

I am concerned on what my laptop can produce that is good for gaming and video watching (resolution and hz wise) with no lag between the two. Obviously I don’t want to sacrifice much quality to the display, but I dont want to get a monitor that my MBP can not handle in terms of gaming. Is there a middle ground that solves this?

Thanks

Iain