There’s only currently really 3 browsers worth testing against, in order of priority:
- Chrome
- Safari
- Firefox (you can use Firefox Developer Edition to develop/test with)
This assumes you don’t care about the mobile experience, and just the desktop experience. Regardless the core browser options for mobile are essentially the same, except Firefox mobile is even more niche.
If you don’t have a Mac, then Safari is off the table, so I’d focus on Chrome and Firefox.
However its worth mentioning that depending on the game and game engine you use, you might only need to use 1 browser and rely on the game-engine to cover up any differences in browsers.