IMO the best option is a newer trinocular microscope model because it will be compatible with various things you will be installing later. I would not go with big name brand, because it’s going to be expensive and the accessories even more expensive and the advantages they offer in optics quality are not worth the extra price.
The question of whether to get an Amscope or a no-name or Eakins trinocular microscope boils down to them being manufactured probably in the same place but Amscope has better quality control and so you will probably get the best quality out of these if you go with an Amscope. But that doesn’t necessarily mean the others are bad. If cost is not an issue, go for the Amscope.
You will want to get the newer version of the body which has the zoom wheel moved towards the front of the body. This newer version has a few optimizations in terms of optics and body design.
Working distance is dictated by the Barlow lens you attach at the bottom. You will mostly be using a 0.5X lens which will give you about 16.5cm working distance to the work surface.
Delay is no longer an issue with these newer cameras that output via HDMI, you can have a small monitor attached directly to the microscope boom arm (I use a 10 inch one and it’s great for me) or a big monitor, the video feed will be real time, you can solder with that no problem.
Camera selection is an important topic if you are going to be using it mainly through the camera feed. All cameras in the $150 range have about the same sensor size and the same performance. A good option in that price range is the HAYEAR 34MP it can output 1080P 60FPS over HDMI.
If you can afford a more expensive camera (~$350), then you can go into auto-focus territory and bigger sensor size. The IMX290 based cameras are great.
You will also need an optical adapter between the microscope port and the camera. For the $150 camera model shown above, the 0.5X adapter works best. If you go for the more expensive, bigger sensor camera, I was told you can also use a 0.3X adapter for increased field of view. This video I did shows has how I installed the 0.5X adapter on my setup.
If you go for the setup described here, you will also need a C to CS ring adapter which is shown in the video linked above.
All of this makes sense if you still need or want to use a microscope the traditional way through the oculars. If you will only be using the microscope through the camera port with a monitor, then you can get away cheaper, easier and in a smaller form factor by getting the Hayear 34MP camera mentioned above, combined with a lens and stand, the image quality will be superb and you don’t need any of the extra bits mentioned above. Or you can just spend extra and get the AF camera in the same setup.
If you do go for a full microscope setup, you might want to checkout this video of mine where I show how to parfocal the microscope for having both the camera port and the oculars in focus at the same time.
And one last note about the AF cameras, some people will find the function annoying because it can focus on stuff you don’t want it to focus on, numerous times. For example you might notice it focuses on your tweezers or soldering iron as you bring them into the frame which will make the pcb go out of focus right when you need it the most. Depending on the model, they do have a focus area which I believe you can control and move on the screen using the menu, that might help solve this problem.