For this purpose Os I think what you bought already is just fine, and
Dishwashing liquid is said to strip wax off, so yes you can go ahead and use dishwashing liquid as you're going to wax the entire car so no problem.
Again for this purpose, the paste NXT will be fine.
Don't bother using the "good" microfiber towels washing or drying, reserve them for removing polish/wax if you don't get a Random Orbital Buffer. Turn the towel frequently so you're using a "clean" area as much as possible when removing wax or polish.