I try to repot when the soil is mostly dry. Moistness and broken roots are a risky combination.
Timing can matter. In theory, I use the exercise as an opportunity to check whether my assumptions about watering are accurate. So I wait until shortly before I would water, take a close look (and feel), and adjust the watering interval as necessary (which for simplicity in my weekly watering scheme would be a 2-fold adjustment in the interval for special cases).
I would recommend a mix of equal parts rock (eg. perlite, pumice) and potting soil (mostly organic), as a starting place for further adjustment. It's a good idea to try to be consistent about the soil you use (with exceptions for special cases) because that will simplify the watering.
