I use a 16" Wacom Cintiq Pro. The advantage that the Cintiq line has over the Intuos line is that the Cintiqs act as secondary displays. There are a number of reasons why I consider this to be a huge selling point.
I can see what I am writing. That is, as I write, I see writing appear "on the page" under the pen. This is in contrast to graphics tablets like the Intuos line, which are essentially mice with absolute (rather than relative) positioning. The couple of times that I have used Intuos tablets, I found them quite awkward and difficult to use (though I image that one eventually adapts).
Having a second display makes it easier to stage work. With a laptop and Cintiq, I can keep multiple browser windows, .pdfs, Maple worksheets, etc off-screen until I want to use them. When I want to show them to students, I just drag them to the the Cintiq. With a third display (such as a cheap television with an HDMI input), I can put my Brady Bunch Zoom squares on one display, my own notes on another, and whatever I am showing my students on a third.
The 16" Cintiq is small enough to be portable-ish—it is not quite convenient for work at a cafe (are we ever going to be able to work at cafes again?), but I can happily pack my laptop and Cintiq into my bag for traveling. If you need something which is truly portable, Wacom makes smaller Cintiq tablets.
[From left-to-right: laptop, cheap television with an HDMI port, Cintiq tablet w/ display.]
Going the other direction, I have also used a setup with a 27" Cintiq Pro, which was amazing. At a cost of a couple of thousand dollars, I'll never get one without institutional funding, but if you don't need portability, it is a wonderful piece of hardware to have.
I'll also note that, as much as I am shilling for Wacom, I have no connection to them. In fact, before getting my own graphics tablet, I spent some time reading reviews of similar tablets from other manufacturers. A good place to start might be with this list of similar tablets.
With respect to software, I have found that Notability works reasonably well as a whiteboard. The main disadvantage of Notability is that it produces monstrously large .pdf files—I suspect that it is exporting high resolution raster images rather than vectorized graphics. I haven't really tried any other software, so I can't speak much to the relative advantages or disadvantages.