There are three terminals at the Airport. You want to park at the one closest the station, that's *not* terminal 3. Give me a moment & I'll check if it's 1 or 2. Note they are doing renovations or something to one of the carparks.
edit: Map is
here - so best parking lot to aim for if you're short of time is probably the one entitled 'voyager' on the map (not the name of the parking though!) or the one between the station and teminal one underneath the 'skylink'.
Now, I've only ever gone to the airport to pick up rental cars or fly so I normally train
to the airport.... the connecting links between terminals 1, 2 and the station are good - you do it all undercover on the 'skylink'. It is a fairly long walk from the one end to the other though, so beware if you're short of time. Terminal 3 is not directly linked, you need to walk outside or catch a connecting bus!
Edit again - prices are
here