My main suggestion is “don’t.”. Use a regular pen and paper notebook. Transcribing and expanding your notes into a computer later can help you retain the material.

Would an old iPad or a Microsoft Surface be a viable alternative?

I’ve loved the Samsung Active series. Practically bulletproof with a remarkably good pressure sensitive stylus and good overall specs. And not too huge

Older Microsoft Surfaces have quite terrible battery life, especially on Linux, have terrible thermals and aren’t very repairable. I’m in the middle of repairing a Surface Pro 7 and the wifi antenna is sandwiched between the frame and the screen, so taking the screen off is a death wish for the wifi antenna (even ifixit ripped it in their repair). The battery is also permanently glued onto the frame, saying that it should not be removed or replaced. The Surface, with an Intel CPU, absolutely fries itself trying to update Windows as well. The heatsink inside seems to use the screen and battery as a thermal mass? I believe modern Surfaces are better in both repairability and battery life.

iPads have pretty decently efficient CPUs and have decent performance - probably doesn’t get as hot as a Surface…

Samsung tablets seem ok too and definitely undercut the two when new

I would recommend getting something older (e.g. Tab S7, S8, S9, S7 FE, S9 FE, or iPads or Surfaces second hand if you don’t have much money - they may come with a keyboard cover which will cost you an arm or a leg when new.

You may also consider flip laptops if you don’t demand too much from your laptop. Compared to iPads and Samsung Tablets, you can use Windows or Linux or whatever. Depending on what you study, that may be important. Flip laptops typically have not great thermal performance so don’t expect amazing normal laptop like performance, but I’ve previously had an Acer Spin 5 and now I’m using a Dell Latitude 7440 2-in-1 and they’ve both been great for light workloads. They’re bulky compared to tablets and I’d only use them on tables, which isn’t a problem for me. I lose out on the higher wattage CPUs used in non 2-in-1 laptops though. Some people describe 2-in-1s as a jack of all trades, master of none, as they’re not great laptops and not great tablets. I’ve personally really enjoyed having everything on one device - online exams could be done in Xournal++, exported to PDF and just uploaded all on one device.

Any of the Samsung Tab S tablets should work. Does double check it actually supports the s pen.