Hi Ryan, welcome to the site.
18 x 18s are pretty big, I hope the floor is pretty dang flat to begin with, or you'll be fighting those tiles to maintain "flat". Start out with a 1/2" trowel, but you need to check your coverage as you lay....that is, you need to pull a few tiles back off the floor after setting them to see how much of your tile is covered with mortar.
What mortar where you planning on using? A medium bed?
Grout size is a preference thing. With tiles of that size, 1/4" would be my starting suggestion.