As has been said already, a 16:9 aspect ratio makes sense since most people have a screen like that.
If you're looking for recommendations: personally I like using 640x360 when going for a somewhat but not too pixelated style. The benefit is that it scales nicely (integer scales) to most common resolutions: 2x scale is 720p, 3x is 1080p, 4x is 1440p, 6x is 4K UHD.
If you're not targeting a pixelated look, you can use practically any resolution (the user will most likely want to play in their monitor's native res). In that case you might want to limit the aspect ratio, though, to prevent the player from seeing things that should be off-screen when using extreme ratios.