She should definitely play the one she loves most - but it's good to think about all the options.
I have girls who have played various things between them. DD1 started on violin and picked up viola later. This was a GOOD move. She's not a soloist and says the violas are always the nicest people in any orchestra (and she's all about the social life when playing, not about being in the limelight at all). Also she loves the way it sounds - but still uses her violin for solo work and folk music, so that's an option.
DD2 is a flautist. As others have mentioned, flute is a relatively easy and cheap start. However, if she does want to play in orchestras and wind bands it is vastly competitive, and though it was cheap, the £3000 flute that her new teacher wants for September is an eyewatering cost for a 13 year old. She is also a bassoonist. Although she picked this up much later it gives her a bazillion opportunities, and it isn't even a nightmare to transport. If I'd known what a bassoon was, and if her school had had teachers I would definitely have suggested she took that one up earlier.
In terms of opportunities, I'd say oboe (small, not massively expensive for a starter instrument, always in demand), clarinet, and then the less popular brass including tuba and trombone. And bassoon, though harder to source.
As an unscientific study I once looked briefly at what the musicians I know had got their children to learn (after all they know what is in demand)
Viola (as a first study)
trombone
oboe
double bass
And some violins...
All of them were quite anti flute as a choice, but DD2 really loves hers!