Generally you use the f-stop and ND filters, if necessary, to control exposure, not the shutter except in extreme cases. You adjust the shutter for motion effects or to sync with the hertz cycle of certain pulsing sources.
Most people shoot 24P in the range of 1/48 to 1/60 to match the look of 24 fps film shot with a 180 degree shutter (1/48th of a second.) 1/60 when you need to sync with some flicker 60 Hz light sources that don't seem to like 1/48th. Sometimes you go to 1/32nd to gain a half-stop more exposure, or even turn the shutter off at 24P, which is 1/24th. You can one-stop more exposure at 1/24 instead of 1/48 but you also double the amount of motion blur, which looks smeary.
Other times you may shorten the shutter time to 1/100 or 1/200, etc. for a crisper motion, either for the "Gladiator" action look, or because you plan on slowing down the footage in post and need less blur per frame or field.
Most 60i video is shot with no shutter, i.e. 1/60th of a second.
I'm talking about 60 Hz country shooting. In 50 Hz countries, 25P and 50i are more common, and 1/50th for the shutter speed.