How to handle continuous values and a binary target?
I am expecting this question is for a supervised learning problem where you have a mixture of continuous and categorical features as independent features and your dependent or target feature is a binary class feature. If that is so please follow the below advice.

There might be a much better solutions but this worked for me. I had more than 200 features and a categorical feature like pin code. 


Target Feature as 1/0


I am assuming this is a supervised learning problem and the best way to go about will be by starting with a basic logisitic regression model.
If you are not impressed by the performance then you can even try some advanced classification algorithms like Naive Bayes, KNN, SVM etc.

Categorical Feature


You can use pandas one hot encoding for this


I kept a threshold, and used one hot encoding only on those unique categories which occurred more than this threshold
The ones which were less than the threshold can be dropped, but I used a special value to encode them just in case to not to loose them.
You can follow here to know how to perform one-hot encoding




I hope I answered at least to a certain extent. Again, I used this solution for my issue and it worked pretty well and hope it works for you too.