There are plenty of options, but most of 'we amateurs' would have had a
Dobsonian ('Dob') at some point, and I think that's what most of us would recommend for someone still developing a taste for the hobby. Dobsonians are also the biggest bang-for-the-buck in visual observing.
A GoTo Dob (i.e. computerised) is, IMHO, best because a 16yo could easily become frustrated and it's a time-saver. Besides, GoTo is cool! Despite some purists arguing the contrary, many experienced astronomers use GoTo.
With a budget of up to $3000, personally, I'd push past the 8 inch (200mm) aperture and go for 10 inch (250mm) - she'll grow into the size. A 16yo should still be able to manoeuvre a 10 inch around a back yard and it will still fit in a small-to-medium hatch so can easily be taken to dark sites. When looked after, that scope will last her at least a decade.
A Sky Watcher 10 inch GoTo Dob lists for around $2300 - $2400, plus shipping, which leaves a few hundred for additional eyepieces (variable cost), a collimator ($65 and up) and a shroud (~$70). Don't bother with expensive covers at this stage - store it inside or in the garage under a small tarp. You may not need the trolley either - a 10 inch isn't that hard to move around.
And now you'll know what to get her for Christmas and future birthdays: more eyepieces!
Here are some listings, but stock seems to be a bit low in places:
Andrews ($2299) -
in stock:
https://www.andrewscom.com.au/site-section-10.htm - you need to scroll down a bit and, under 'Telescopes ...', click 'Skywatcher', then scroll down to about half way down the page to
10" Computerised collapsible Dobsonian with Wi-Fi.
AstroAnarchy ($2395) - out of stock:
https://astroanarchy.com.au/collecti...nian-telescope
OzScopes ($2399) - appears to be out of stock:
https://www.ozscopes.com.au/skywatch...telescope.html
Edit: Optics Central (MEL) ($2399) -
in stock:
https://www.opticscentral.com.au/sky...telescope.html
Edit: Sirius Optics (MEL) ($2599) - out of stock:
https://www.siderealtrading.com.au/p...ble-dobsonian/
Bintel and Testar (two other well-known retailers
Edit: that usually carry that telescope) don't currently list the Sky Watcher 10 inch GoTo Dob (probably due to stock issues).
Once you've got the Dob, come back for advice on any extras you may want.
You mentioned astrophotography, but the costs rack up there very quickly, as does the time commitment. If she really wants to go that way, that's a different conversation regarding what-you-can-get-for-$3000.
You are indeed an awesome parent!