I have these skills which would the the most useful to get next. My detective is smart and charming.
I have theses:Thread Analysis, Advanced Thread Analysis, Hair Analysis, Sweet Talking
Rule Bending (helps with getting the townies to be more cooperative), or Research (let's you eliminate a suspect with a fake/none-of-your-business alibi) - and after that Rule Bending and Sweet Talking all the way up to Advanced :)
Oh, and Flirting too - gives Rule Bending and Sweet Talking an increase of +20 when talking to the opposite sex.