You're question on the wood was answered so I will try to help out on the saw question. There is no reason a bandsaw won't work. A lot of that depends on the saw and the operator. A tablesaw will generally be faster, more accurate, and easier to use.
A 14 inch bandsaw will be limited in blade width. A wider blade will give a cleaner cut. You will probably get a somewhat jagged cut with your saw. If you have a jointer and a planer that won't be an issue at all. Assuming your lumber is straight you could get by with just a planer. Rip the strips over size, joint or plane the board and rip another strip, and so on. This will give you strips with one good face. Set the planer to 1/4 inch or whatever thickness you want the strips to be and run them through. This will give you very accuratly size strips.
With the thickness of your stock I would first re-saw it to about 7/8 and plane that down to 3/4. Then rip off your 1/4 slices.
Hope this helps,
Mike Boren