For a new bike,
Frame
Wheels
rd
crankset
shifters
fd
cassette
saddle
chain
saddle
tires.
Upgrading an existing bike (given that you already have a frameset):
tires
wheels
rd
shifters
crankset
fd
cassette
chain
For me, the least important is the chain and cassette, even the lowest end (105, Veloce) cassette and chain will work with the higher end, and has the poorest return in value when it comes to performance if you spend more.