First, the best thing that you can do is to seal the grout. Buy a bottle of silicon tile sealer and follow the instructions carefully. it will bead up the water and will keep algea and gunk from turning the grout green and black.
Grout is very porous and will collect all sorts of growth, the sealer will seal it up.
I would definately try to discourage you from painting the tile. I have seen too many either shoddy jobs or where the paint just releases in sheets.
Now if you do paint the tile, do use the two part paint product and you are right, the product has ether in it to make it self level and dry fast, but it can be very dangerous to your lungs if you do not proper ventilate. This stuff is serious.
now, this is my opinion and others will and may disagree, but its a starting place.