Budget note-taking tablet/laptop recommendations (OneNote)

Hello all, this is my fist post on the forum! I'm looking for some help with purchase advice/recommendations. I am a college student looking to get a device for in-class note taking, studying course materials and notes, web surfing, and personal productivity applications.

My three criteria are:
1. I can easily take digital handwritten notes on Microsoft OneNote
2. It will complement the functionality of my current main laptop, a Lenovo IdeaPad Y580 (Windows 10)
3. Will run under $300, the cheaper the better

A few other things to consider:
I would be perfectly happy with older model or used devices to get better functionality at less cost.
I am studying engineering, and need to use MATLAB and Solidworks for some of my classes, but I realize it's unreasonable to expect a product in this price range to do that, so I am planning to use both my IdeaPad and this new device for school. Therefore, I don't need a do-it-all device, but more something that will add a portable note-taking and productivity functionality to my current setup. My phone is a 2nd gen Motorola Moto X Pure, so if there's any complementary function there, even better.
Finally, I'm not sure what size device would be best. I like the idea of portability, but 8" tablets seem a bit small coming from taking notes on full-sized paper. If you've taken notes on something like that please let me know your experience.

Thank you for reading through this and for any help or feedback!

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Clarification Request
Hmm, laptop? and the other I found with an i7 look very nice for 300.

I did pick up the Amazon Fire 10 HD for not much and then I could install OneNote after I add the Google Play Store as follows:

I did that already to my Amazon Fire HD 8 so here's OneNote on that. was just under 60 to my door. It's more for testing what we can do with it. Since it's just 16GB I'd plan on adding some 32GB card to it soon.

The 8 inch in the above picture was just under 40 at but since I got that a while ago it has some 32GB card in it and I already installed the Play Store so I could install OneNote to test for you.
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The 10 inch Fire is back. It's 60USD.

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