I've been using the Pilot Frixion pens for quite awhile now. They work great, are affordable and you can get various colors. You can also find them at places like Target.
I have an air soluble marker, the lines fade pretty quickly especially if there is hot/humid climate. I found they fade also with contact with the skin and some warm water. They last between 4-5H to 24-26H depending on a lot of things. For the water soluble one I can't recommend any but if you don't want to regrid the project everyday I would use the Bohin mechanical pencil that comes in very different colors, I prefer the white and green leds.
I dont use air soluble pens. I grid when I have my project on stand so it usually work for weeks I think I'll get annoyed pretty fast if my grid will disappear on me & instead of stitching I'll have to re-grid. So I use water soluble & uron soluble which stay on fabric for years if I need them to
i alwaxs use blue (only blue - not any other color) water soluble pens and never had any issues with it. I always wash my finished projects, so i don´t care about the water pens