1) I generally dive reefs and wrecks not exceeding 90 feet, and alternate between an AL80 and steel 130. I would like to be able to run doubles for something deeper like the Spiegel. Is there a single bp that I can use to accommodate both set ups?
The same backplate and harness can be used for singles and doubles, but the wing needs to be different. There are wings that are touted to be good for both; they make compromises and turn out to be really "good" for neither. One thing to look at, if you are going to run both, is whether the plate you intend to buy has camband slots or not. If not, you will have to buy a single tank adapter for your rig. Some people like them. I view them as one more piece of equipment I have to deal with and remember. I prefer an STA-less setup, like the one DSS has. I believe Oxycheq also has something similar, and Halcyon at least used to.
If you are diving primarily warm water with little exposure protection, you will definitely want an aluminum plate, to avoid being overweighted with the 130 or with doubles.
2) The one part of my bc I like is the integrated weight system. Is there anything like this available in a bp? Or do you just use a belt?
There are several ways to get an "integrated weight" type arrangement on a BP and harness. Halcyon sells their ACB pockets, which slide onto the waist belt. They do use up significant territory. I can't remember if it is Zeagle or XS Scuba that sells a weight pocket that slides onto the harness. It loads from the top with a zipper, and releases from below. Or you could use a DUI Weight and Trim harness, which is what my husband does. In any case, such a system is an additional purchase.
3) What is an inexpensive yet quality bp set up to consider? I am guessing I would need aluminum plate, as the ss with a steel tank may be overweight.
Given where you are, I'd look into Dive Rite, although be careful choosing a wing.