Here in the PNW cellulose is not considered the best option, it's a mold disaster waiting to happen number one. Also, it settles. In my remodel experience, I've seen settling as much as 2" in stud bays in as little as ten years.
Blow-in fiberglass would be a better option.
But, what is the moisture barrier between the brick and insulation going to be? Unless the brick is painted this could be a problem. Spray foam usually provides its own moisture barrier. If the studs are all exposed you will want to design a moisture/vapor barrier into your plans. If not you might have to wing it.
Renters are aware, or can be educated about, the utility bill benefits of good insulation.