Does she have a favourite magazine? If so, how about a subscription to it, the gift keeps on giving and if she is anything like I was at 14 she will love magazines but hate spending money on something she will only read a few times and will quickly become outdated.
Make-up? A lipstick in a shade you think she would love?
Can you get her something small just from you? It might be a bit soon to be doing a 'joint' present from you and her dad. Perhaps a 'girly' (toiletries/chocs/flowers) type of gift similar to what you might get any other female you don't know that well.
The activity/cash side of things is your partner's responsibility so, however well you want it to go, I'd suggest leaving that to him to sort. Obviously be encouraging but he's know these kids for a lot longer than you and has a duty to them. You don't - and they probably wouldn't feel right if you acted like they did.
I would like a little help as have just met my partners children and my 3rd meeting will be his daughters 14th birthday. She is extremely hormonal(!) and hates the world although can be very sweet. My partner left his wife 3 years ago and has been spoiling the kids out of guilt so she is used to being showered with cash. My partner is not able to do this at the moment as unbenown to the children his business is struggling. I would like ideas of what to do as we are all spending bank holiday Sunday together (plus 16 year old brother). She is a picky eater and they went bowling a week ago. SHe is obviously still trying to suss me out as I am 14(ish) years younger than her mum, (late 30's) and have no children of my own. All suggestions welcome.