Joe there are 2 things you need to remember about stair layout max riser ht. is 8" (7 1/2" norm) min tread 9" (10" norm)this is what you cut your stringers at.
Take your total height floor to floor and divide by 7.5, you will get for example 14 plus/minus a few inches, this is the # of risers. Take the leftover inches and divide by the # of risers, add or subtract to 7.5...this is your riser height.
You need to have 6'8" of headroom above your stairs from the landing to the beam you mentioned, that will be about 11 risers (@7.5") The stairs need to be at least 3' wide with a 3'x3' landing...you will need 100" to your landing with 10" tread, you could shorten that to 90" with 9" treads remember your actual step will overhang 1 1/4".
I can just about do stairs in my sleep, however trying to explain how to do it is not my strong suit.
For your stringers, purchase 3- 18' 2x12's, take a framing square, some small c-clamps, and 2 small blocks of wood. Lay the square on the 2x12 (point into 2x12) with the short leg facing away from you and the long leg to your left. On the edge of the square closest to you, on the short leg find your riser height. On the long leg find your tread length. Clamp the blocks to the square, now you can step out the stringers.
Start at the left end of your stringer and step out the steps, marking with a pencil as you go (you will have a bunch of triangles). When you are done, remove the blocks from the square, go back to the left end and continue the line for the first step under the next tread (cut off here). Go to the last riser, continue the line down, (cut here) Now cut out each of the triangles. Check for fit, use this one as a pattern and trace your lines to your next 2 stringers.