Definitely buy used! My supervisor at the museum I work at said microscopes depreciate faster than cars. I ended up getting an Olympus (SZ51 I think) for around $750. It was in great condition and that’s about half retail price. This ended up being the same model we use in my college biology labs. Here’s some photos I’ve taken with it via a cheap Samsung.
Light source may be important, but depends on what you’re doing. Mine came with a ring light that works great, but at school we have built in lights that plug into a unit where we can control the light intensity. We’re working with live hydroids on that though so temperature really matters. At home I’m mostly doing dry mollusks so it’s not as big of a deal (but I’m also starting to do dissections so that might change my needs). At my museum we use the fiber-optic source but I always thought those were super annoying to use.
Obviously binocular is best and an adjustable zoom is very nice. One way to check microscope quality is to see how much the frame moves side to side as you change the focus (check with one eye, good scopes don’t shift much). And a fun thing you can do with a lot of scopes is take out the eye piece and use it as a quick magnifying lens.
In the end it’s a lot of personal preference. Olympus is a solid brand, but Leica and Zeiss are some nicer options. My research prof has a Leica that she can take pictures with from her phone or laptop which is pretty cool (I used it to photograph this and this. Nikon is also decent. Everyone I’ve seen has something different for what they need and what they like.