I think having a hard-coded drop down for actual licenses is a good idea, because then we can do the searching and filtering you suggest.
I don't like grouping them into 'types'. I think that's too much of a value judgement. Any enterprise's legal department is going to approve or disapprove of specific licenses, so that's what developers like me will be looking for.
Potential issues: * Modified licenses (eg: JSLint's MIT + "do no evil" clause)