Hmmm...
Frame and wheels. Frame for the fit and the style (townie, racer, endurance, touring...) but also the wheels as they have such a large impact on the overall feel; they connect all the rest and YOU to the road/trail. You can make a great change to how the bike feels with a wheel change. Just look at the pros- TT is one wheelset/type, climbing is another, another for the flats...