TBR does not really offer an in-depth "solubility rules". There is a list of 5 rules on pg. 186. Those are pretty simple to remember. +1 cations, -1 anions, NO3-, and SO42- are soluble. -2/-3 anions are mostly insoluble, oxides and hydroxide anions are usually soluble. The rules are for the most part "in general" and have exceptions, also the priorities are mostly in the above respected orders.
In the end, this can maybe get you a point but I believe it's more important to understand the differences in molar solubility vs. solubility products. Also focus on the experimental stuff like Ion Exchange columns. I did well on the TBR Equilibria passages and I did not remember very much detail from the chapter. The main points at the beginning is what you really want to understand inside and out. Finally, bring your curiosity to the passages, focus, and you'll do well.