As for how much of the screen it should take up - that's up to you.
As for the dimensions, you want the image to be close to what they will be when it is output by MixEmergency.
For example, if you wanted a square logo to fill an 1/8th of the width of the screen, and had your external display at 1080P (that is, 1920 x 1080 pixels), then:
1920 x 1 / 8 = 240
So, you could have your logo as little as 240 x 240 pixels.
Comments
As for the dimensions, you want the image to be close to what they will be when it is output by MixEmergency.
For example, if you wanted a square logo to fill an 1/8th of the width of the screen, and had your external display at 1080P (that is, 1920 x 1080 pixels), then:
1920 x 1 / 8 = 240
So, you could have your logo as little as 240 x 240 pixels.