1. Congratulations.
2. Welcome to the OB.
3. Talk about jumping into things head first!
I'm not going to lie, if you've never grown orchids before, or if this is just a casual hobby for the both of you. I'd strongly reconsider buying any of the myriad of orchids commonly referred to as "leafless orchids" or "Ghost Orchids".
Like the others have said, there are jewelry pieces that might fit the bill.
As was mentioned, all "leafless orchids" are are a mass of roots wrapped around wood. Maybe, there might be a few occasional small leaves (when I say small, I mean almost - but not quite - vestigial looking) that can or may drop. These roots are usually no larger than 3 mm - 4 mm in diameter.
The majority (more like almost all) of the photosynthesis is done by the roots.
All the "leafless orchids" are novelties. Once the novelty wears off, will you or your girlfriend still like them? IDK.
For someone who doesn't grow orchids, they may look at them and say, it looks like a spider or a bunch of worms.
Anyways, on with the show...
Oak Hill Gardens may carry the actual Polyrrhiza (Dendrophylax) lindenii (this species is the true Ghost Orchid), but let's face it. Many people are not able to grow this plant very easily and very well.
I don't have any experience with Dendrophylax funalis so I can't advise you there either.
However...
I do have experience with
"Asian Ghost Orchids". Namely Chiloschista spp. and Taeniophyllum spp.
Some people are actually able to grow Chiloschista. From what I gather, Taeniophyllum is not that hard to grow either...for a "Ghost Orchid" (in other words, I'm speaking relatively - without any experience, you'll get frustrated and quit).
I currently grow what was sold to me as Chiloschista parishii (I'm not sure it really is what they labeled it as, of course I haven't bloomed it out to know for certain either).
It took me a few tries to get it right though.
Chiloschistas are much more attractive "Ghost Orchids" in my opinion and more reliable bloomers than the actual Ghost Orchid (Polyrrhiza lindenii).
My Chiloschista sp. shows evidence of flowering multiple times in the past.
There is also relatively more cultivational information available about Chiloschista spp, than Polyrrhiza spp.
Although Taeniophyllum spp, have the potential to be very floriferous, they're very small flowered. I had a species where the flower was no more than 3 mm - 4 mm in diameter (not exactly a show stopper).