How about a refurbished Lenovo Yoga?
Runs Linux well, comes with a pen, you can have it folded as a tablet or with a keyboard to take notes. Battery might not last as long as an Android tablet. But is way more powerful and fits perfectly in your budget if bought second hand / refurbished.
Edit: I bought a Yoga 460 back then. Used it during lectures. But soon realized typing notes was faster than a pen. Except for calculus and linear algebra. You should learn latex or use a pen for that. Otherwise, would recommend a Linux convertible over an Android device.
I think with linux, rnote or xournal++ work well for taking notes or annotating pdf.