If you have a good nursery in your area, they'd be my first try, Liz. They'll have the varieties that do well in your area. Don't expect to find any kind of a selection at a big box store.
As far as doing the job economically, yes, the idea of buying maybe gallon size pots and dividing them is a good one, providing you don't try to divide them too small. Try one pot first, divide it in maybe 3 or 4 pieces max, pot them up, keep them well watered in the shade and give a little diluted water-soluble fertilizer, until you see new growth starting. That's how you know you've succeeded.
Depends upon the grass type, but some really only thrive once they have clumped up fairly large. So you might try this with all the types you like, and it may only work with some of them. If you only get one or two clumps going, you can try to take divisions again in the fall once they've had the summer to grow.
