Katie,
I have a couple of suggestions:
Fit your bike to you, not the other way around. If you have a photo of you on your bike, email that to me or post it if you like. Provide two photos: one with the pedal at the 9:00 position and one at the 6:00 position. There are a lot of methods out there. Do a google search for "bicycle fitting" and try out some of the methods.
That said, here are some standard protocols. First, you need to adjust: seat height, seat fore/aft, and seat tilt. Then, determine the distance from the seat to the handlebars. This may require that you replace the stem with the proper length stem. Finally, adjust the angle of the handlebars.
With your shoes off and the pedal down and the crank arm in line with your body, the bottom of your heel should be just at the top of the pedal with your leg straight. Alternatively, the distance from the top of the seat to the top of the pedal should be 1.10x the length of your inseam. Measure this, don't use your pant leg for inseam.
For fore/aft, with the pedal at the 9:00 position, your knee should be over the pedal.
For handlebar reach, one idea is that you should look down and your view should line up the handlebar with the front axle. But, this is somewhat personal.
Also, I used to have lower back issues too. After I started doing deadlifts, I have zero back issues. Maybe it's coincidental...
Good luck and keep us posted.