How to cluster categorical and numerical data in the same dataset?
You can use one-hot-encoding for all categorical features. Then normalizing numerical features (as one-hot is 0 and 1 then maybe normalizing your numerical data to [0,1] will bean intuitive starting poit). Then apply a dimensionality reduction technique as probably you will produce a sparse matrix with maybe considerable number of dimensions. Then do your clustering (try at least two different one. I would say k-means and DBSCAN).

A nice intuitive replacement to one-hot-encoding is to replace values with their fraction. For example in column gender you have 60 male and 40 female, then replace male with 0.6 and female with 0.4. The only drawback is when the number of categories are equal in a column! You need to be careful about those.