The clay I bought can be fired anywhere from cone 6-10, and all of my glazes I'm considering are either 6 or "5-6"
Are you making functional pots with this clay? A ^6 clay can't go to ^10 without bloating or warping and a ^10 clay will be underfired and porous at ^6. No worries if it's for sculpture but not advisable for functional pots. A clay rated at ^6-10 might be okay at the higher temps but not at the lower. I would look into a clay rated as ^5 or ^6 if you are using glazes in that range.
As dhPotter said, since you are considering ^5-6 glazes then I would get 5, 6, and 7. For bisque I go to ^04 (for a ^6 or ^10 clay) For a sitter use bars, for witness cones use the full size regular or freestanding ones. (regular ones are cheaper and it only takes a few minutes to make the clay bases to place them in, just get the angle right). For the glaze firing I would use a ^6 bar but watch the witness cones.