Some thoughts:
a) I'd suggest there is no need to pay anywhere near that amount of money. Maybe 10-20% of that figure.
b) Check if you have a local astronomy society, they should have a variety of different equipment you could try out. (Although probably not at the moment.)
c) From what you've said it sounds like you are in a good location for observation, and just taking something out into the garden should be fine.
d) There are broadly two types of telescopes, refractors and reflectors.
i)
Refractors are what you probably think of when you hear the word telescope. A long thin tube on a tripod where you look in one end and see out of the other.
Generally refractors are better for magnification, so things like viewing craters on the moon.
A refractor on a bad tripod will be very frustrating, as it will wobble around too much to actually be able to see anything. Don't skimp on the tripod.
Refractors are much smaller and lighter, so easier to transport around if you are leaving the house to observe.
ii)
Large reflectors are much wider tubes that sit on the ground in their own mounts. You look in the side.
There are also smaller reflectors that also mount on a tripod, and table-top versions.
Reflectors are generally better at collecting more light at less magnification, so you can see dimmer stars, nebulae and so on.
Reflectors are much more stable on their bases than refractors, and the telescope and (non-tripod) bases are a much simpler design, so you end up spending proportionally more on the functional bits of the telescope and less on the mountings.
As with any device, the best one is the one you (or your daughter) would actually use.
So I'd suggest smaller and lighter rather than bigger and heavier, that way you/she can just take it outside whenever she wants.
(I don't have kids, so I've no idea how much weight a 13 year old could carry
The telescope I link below is about 6kg.)
And I'd suggest a refractor with base mount rather than a tripod, as they are easier to setup and less prone to wobbling.
Normally I'd suggest going to some shops, or even better finding an exhibition to go to, but not really an option at the moment.
In a similar situation I think I would consider something like this, a smaller table-top refractor:
https://www.skyatnightmagazine.com/revi ... dobsonian/This should be a reasonable balance of good enough to enjoy using, without being too expensive if it turns out not to be her thing.
f) If your daughter is also into gadgets, for both types of telescopes you can pay more to get computerized mounts, where you can have a phone app linked to the telescope, select what you want to view on the app and have the telescope automatically track to that point in the sky. For astro-photography you can also get mounts that automatically adjust for the rotation of the earth, so you can mount a camera instead of a viewing lens and take long-exposure photographs.
g) Also consider a good pair of binoculars as a cheaper introduction.
While not as good as refractors for magnification or reflectors for light collection, they are easy to carry around and use.
Avoid going for ones with too much magnification or too large objective lenses, they won't be useable without a tripod, especially if this is for someone younger, who might not have as much arm strength.
A sun-lounger is actually quite a good tool for binocular observation, it is earlier on the arms and neck to lie down with your neck supported and look almost straight up.
A reasonable pair of 10x50 binoculars would be good enough to start with, and also useful for other things as well.
For a pricer option you can go for image-stabilized versions, which tend to have smaller lenses, so collect less light, but make up for it by automatically stabilizing the image while you hold them, allowing you to actually see dimmer things that you would otherwise. They also work as excellent bird-watching binoculars. (I have a pair of Canon 10x30 IS binoculars, I really like them, but they are pricy.)