A mouse that surprised me alot which i got years ago and i checked you can still get was the Cherry MW 3000.
It was pretty cheap for a decent wireless mouse with around 15-25 bucks depending on where you get it.
The thing that surprised me the most was how long the batteries was lasting which was 2 AA batteries and lasted about a month to 2 month with an average use time of about 5-15 hours a day.
Has 2 side bottons for going back and forth on websites which sure also can be used for games.
If you wanna couch game it was working ok with being about 7-8 feet away after that it wasnt really great.
It also has a dpi switch changing it from 1000 to 1750 and vice versa which can help in games depending on what you are playing to go from fast moving to a more precise one.
In case you wanna store it away or take it with you the nano usb plug for the reciever can be put beside the batteries and it wont get lost that way.