I'd wait on the laptop, if you don't already have one. I have found almost all of the classes I attend forbid using them in class. I can use a tablet when researching at the library, and I can pull most papers from the library electronically from my home or office. I also read papers on my tablet, like an e-reader. I have a desktop, a laptop, a netbook and a tablet, and I rarely use anything but the desktop and the tablet. I also still print out most papers and make notes and highlights by hand. YMMV.
On filing vs scanning: I scan my own returned papers to archive. But I wouldn't scan student papers. Keep the hard copies. Just box them in banker's boxes and alpha order by course and term. You can toss the whole box when the storage period ends. That's how most of my profs did it. I would think unless you have a fast auto-feeding scanner, scanning all those papers by hand would be insanely time-consuming. FWIW, most print and copy shops will fast-scan for you for a very reasonable fee. So if you want to scan whole boxes at the end of a term, consider taking it to be done.