I have a USB microscope similar to this one. (I won't post a link otherwise this might seem like an advert - there are many similar products and I think they're probably all just as good.)
You can find similar products sold as microscopes, otoscopes or endoscopes, and adding "USB" to the search terms will tend to help.
The image quality is surprisingly good for something in the US$20-$30 range. It has a manual focus ring (no autofocus, but for macro work you probably don't want that) and a built-in light. It can focus anywhere from touching the lens up to I guess 20cm or so away, so there's no need to prepare slides or anything. The computer sees it as a normal USB web cam, so I never had any software issues with it at all. I use the built-in app "Photo Booth" on a Mac and it just appears in the drop-down list of cameras.
If this is for photography (i.e. if you want to produce "good" images) then you might want to spend more, but for your stated goal of clearly resolving millimetre-sized objects it might be more than good enough.
Here's an image to give you an idea. Not a professional quality image, but clearly legible. These are Japanese rice fish eggs. I don't know their exact size but they were quite a bit smaller than 1mm. I believe the small dots inside are the blastocysts (the first few stages of cell division), so I guess they're pretty small.