Having difficulty writing a "best-fit" query..

Hi list,

I have a many-to-many relationship between movies and genres and, in the
link table I have a third field called which orders the "appropriateness" of
the relations within each movie.

For example:

movie_id, genre_id, relevance (i've used movie/genre titles for clarity
here, but in reality they're id's)
--------------------------------------------
beverly hills cop, action, 2
beverly hills cop, comedy, 1
the heartbreak kid, comedy, 2
the heartbreak kid, romance, 1

The above would mean, to my application:
"Beverly Hills Cop is both an Action and a Comedy movie but primarily an
Action movie."
"The Heartbreak Kid is both a Comedy and a Romance movie but primarily a
Comedy movie."

First of all, if there's a better way to model this kind of ranking/ordering
of many-to-many relationships, please let me know.

Now, to my problem..

I'm taking a subset of all my genres, and I want to get ONE row for each
movie in the subset alongside its most appropriate genre (whichever has the
highest relevance). In other words, the best fit.

I've had a few goes at writing this query but I can't seem to get it right..
The theory in my mind is to:

1. filter the link table down to rows that fit the subset of categories
(easy)

2. filter the link table further to keep only the max(relevance) for each
movie_id .. this is where i'm having trouble.

If someone can shed some light on this for me, I'd really appreciate it.

Thanks for your time,
Jamie