Dropout classifcation I have a data set of recruiting pipeline information that has 12 columns of categorical variables (they range from binary variables like gender to non-binary variables like the name of the school the applicant attended). The last column (13) contains a "Yes" or "No" value that tells if the person is still in the recruiting process.

The idea here is to build a model that can predict (reasonably well) the likelihood of the person withdrawing from the recruiting process at any given stage (there are many stages and this field is one of the 12 independent variables captured).

I was thinking of using logistic regression to create the model but all the predictor variables are categorical, which I hear, doesn't bode well for logistic regression. Another factor is that some fields have missing values (like gender) that I cannot reasonably input/capture accurate data for atm.

Given my situation, what approach do you think would be a good starting point? 

Was thinking of random forest but not sure if there's a better way to go about tackling this problem.
There isn't a particular approach or model that is definitively the best. You might want to try multiple types of models. A good starting point would be to visualize your data. If there are many non-linear relationships between your data and the the outputs you are predicting then you might want to start with a tree based model. It will be much less work to make it perform well. If the relationship between your variables and the outcomes you are predicting are fairly linear then a logistic regression model is a good approach. 

If you have to have a silver bullet model to solve all your problems then I recommend trying xgboost. Use grid search and you will have a good model.

I actually worked on a similar project for my university. Aggressive feature engineering combined with logistic regression performed and xgboost were the two best models.