Is regression or ANOVA the right approach for determining RRP based on a set of RRPs associated with categorical variables
ANOVA is a linear regression...a regression on categorical variables.
Regressions can have any mix of continuous and categorical variables. Some, like ANOVA and ANCOVA, have special names that you may want to use when you're communicating with people who have less training in statistics and don't know how to unify them with linear regression.