This has been discussed before and there wasn't a total agreement (why doesn't that surprise me??).
It will all depend what sorts of playing you are intending to do and where you are based.
I got a cornet second - at the time I was playing with a brass band. This was followed by a soprano cornet.
After that came an Eb/D because I had started doing more orchestral work and found the to be very useful for what I was playing.
A common second instrument seems to be a C trumpet (if you are in the States and college bound), but over here we are mostly Bb players (although that appears to be changing in some areas).
I like the Eb/D as a second instrument - it is not as difficult to master as a piccolo (which is an instrument I think most players go onto too early) and is perfect for when you find yourself playing 3rd parts in Bach (where the notes lie too low for a piccolo and the sound of the C is not what is required). There is very little in the "starter" piccolo repertoire which can't be played very effectively on a D trumpet.
If you are more jazz based, the flugel is probably a good second instrument.
So, it all depends on what you are looking for
Purely personally:
Bb
Eb/D
Piccolo
C
Cornet
G
(for orchestral)
Bb
Cornet
Flugel
Soprano Cornet
(if you do brass banding)
Bb
Flugel
(if you are jazz orientated)