You're generally going to get more bang-for-buck buying a used clinical microscope (or similar), but something like a lot of Amscope's new offerings are also good choices. For a camera, you can use a cell phone camera (ideally with a holder for consistent alignment) on an eyepiece, a dedicated eyepiece camera, a microscope with a dedicated camera port (usually a trinocular port) and its own camera, or an entirely digital microscope with no eyepieces that you just look at on a screen.
There's a huge variety in what's available and without some experience using one or some basic knowledge of how they work it's going to be difficult to explain or differentiate features/models, but as a baseline:
Magnification quotes basically don't matter. You probably want 10x eyepiece(s) and 5-50x objectives or thereabouts. Most higher power objectives will require a coverslip and oil immersion to achieve their full performance and you run into the rayleigh limit for typical objectives above 50x or so, so while higher powers (or higher magnification eyepieces) will make the image you see bigger, it won't be sharper (it can't be because of the physics involved without fancy, much more expensive methods.) To that end, a stereo microscope or a variable focus one (usually a single larger objective) will have trouble zooming in enough for diatom ID and such, but is great for more space to work and looking at larger things like copepods or larvae, and what people mostly think of as a microscope (multiple objectives on a nosepiece in an upright thing you have on the table) is better for very small things and has more trouble looking at larger ones (you'll have a few millimeters field of view maximum.) For total magnification (objective times eyepiece), 10x or so is where you start for amphipods and corallites and things, and you're unlikely to need more than 400x or so unless looking for bacteria or small eukaryotes.
Even inexpensive modern optics are pretty good, so look for build quality (glass lenses for sure, ideally a metal body), a bright light built in (the more zoomed in you get, the less light is available in the field of view), and a stage/focus adjustment that doesn't slop around and holds its place (there's usually a tension adjustment for the latter.) If you want better optics, look for objectives labeled PLAN or Achromat (for a flatter field and better color correction respectively) over your base objectives. There are better still, but when you start getting to fluorite or apochromatic objectives, you'd spend your whole budget on one.
Make sure you get yourself microscope consumables - slides, coverslips, immersion oil (if any objective is marked oil), maybe some stains or an example slide so you can practice finding good focus and contrast. Slides with wells are convenient for larger organisms, but the depth of field of a higher magnification objective is so narrow that it will be a hindrance over about 10x or so, so generally you want a drop of liquid sample with a cover slip on it, and then I often wick that liquid out from the side to get less thickness between the slide and the coverslip. Also worth getting some kimwipes (or similar optic safe lint free wipes) for wiping off glass.
If you end up getting a camera or going with a digital microscope, make sure you're considering framerate when choosing. If you get a USB 2 camera, for example, any reasonable resolution will be a low enough framerate that you won't be able to see continuous motion, and it can make centering your target more annoying. With enough light and a global shutter, that shouldn't mean image smearing from fast moving targets, but that can come up too. Something like a USB 3 camera or an HDMI/VGA output should have better framerates and be more enjoyable to use casually (at least for me.)
Generally, for regular microscopes, binocular viewing is the standard for anything beyond the base level, but some people have trouble merging the images between both eyes (it is also a skill you can develop), and some prefer just to look at a screen. If you have binoculars, you can also have a manual view and a camera of some sort, though you could just get a trinocular for that as well.
Finally, it's definitely a skill to look through a microscope and get your adjustments right, as much as its a skill just to mount your sample, so expect to practice. This can be looking and more mundane things, random things in your tank, or prepared slides. There are some advantages to getting a prepared, stained slide (even a cheap one), becuase you know there will be distinct features of a certain size to see, and you can practice finding focus, appropriate lighting, and the settings for best contrast to see (and on your camera), so that when you have some nearly clear, always moving sample from your tank you want to see, you know how to track it down and get a good view.
The hole is deep in the case you want to dive in, but it's largely unnecessary for most reef investigations.
Just grab one of the led ones off of amazon. I have thus one but they have newer versions...it's all you need and much easier than a regular microscope or stereoscope
TOMLOV DM602 HDMI Digital Microscope with 3 Lens, 10.1" Soldering Microscope for Electronics Repair, LCD Coin Microscope Full View, 2K Video Microscope for Adults, Biological Slide Microscope, 64GB https://a.co/d/2qYNy4j
You can zoom in as far as needed for dinos or pods or whatever..but here's some quick pics.
Even without a fancy hookup for your camera you can still get decent video
This was taken by me on my iPhone at work of Costia (Freshwater parasite) at 100x
Not sure the microscope brand it’s just a normal looking one that you’d see in any high school lab nothing super fancy
Great thread, thanks for all the replies and suggestions! I'm going to check out the AmScope, looks like it might be a good value. But tagging along to see what else is suggested.
This seems crazy cheap but I think it could do the job for basics... thoughts?
LAKWAR Portable Digital Microscope for Kids & Adults, 200~1000X Pocket Handheld Microscope with Slide Kit, Photo and Video Capture with 2’’ HD Screen and 32G Micro SD Card https://a.co/d/9EJQ6tR