The type of tree you need is defined by the type of output. If your output is numeric ("numeric" here means that you can do greater and less comparisons and compute a meaningful distance between values), regression tree is the right choice.
For either type of tree, you need to convert your inputs to a numeric matrix. Then you can indicate what variables are non-numeric (categorical) using the 'CategoricalPredictors' parameter; if all your variables are categorical, set it to 'all'.
You can convert your non-numeric data to numeric in many ways. One way would be to use the categorical class in MATLAB on each variable in your data, for example:
>> colors = categorical({'g' 'r' 'b'; 'b' 'r' 'g'});
>> numeric_colors = double(colors);
Then use the new numeric variables as columns in the matrix you pass to the fit function.
