A "Spotting Scope" is probably the most common term that I'm aware of in the UK.
You very much get what you pay for in terms of optical quality, but since your main use seems to be indoors, you might save some brass by looking at older second hand non-weather sealed scopes.
Again, for indoor home use, size/portability may be less important, and a larger size does make for brighter more relaxing viewing.
My weather resistant 80mm one is an Opticron, which oddly I normally leave at home due to its size.
I also have a couple of older Kowa models which Jane and I use from bird hides.
The latter are noticeably better optical quality, and feature Fluorite Crystal front lenses rather than glass, though being older models aren't waterproof.
I do have a couple of smaller ones for holiday use, but nothing like as good a quality; had they been my only scopes, I could well have been put off the whole idea of owning one at all, whereas I just accept the convenience for travel use.
Prime eyepieces seem to offer better quality than zooms, certainly cheaper zooms anyway, though I do prefer a zoom eyepiece for convenience. The actual zoom eyepiece is often matched to the size of the front element as the overall magnification can vary.
If you're thinking 30x zoom, in the cheaper ranges anyway, maybe look for something with more magnification as many zoom eyepieces will perform better at the less extreme magnifications.
My own scopes are all straight, unlike Michael's 45° prism one; I prefer straight through for home and bird hide use, as I'd normally be sitting down.
The angled ones though really do come into their own when outdoors with a tripod; on the one hand the tripod doesn't need to be as tall to get the scope to eye level, but also you don't crick your neck when looking high into trees.
BirdForum is worth a read for reviews to give you some ideas.
https://www.birdforum.net/reviews/
With care you shouldn't need to spend a fortune, if you go second hand, and if you don't like one or want to upgrade, you should be able to cover your costs by selling it on (maybe even make a small profit)
Bill