If you do end up typing up your notes, I recommended using Microsoft OneNote. It was designed with the student in mind and does its job very well.
Usually, instructors may post skeleton notes as a PDF or ppt or the like. Download these and put them right inside OneNote (you're essentially 'printing to onenote' here), you can ask me for details if you'd like. So basically what this does is put in every slide into OneNote as a picture, and then you can type, drawing, and record sound all in one place. Aka you don't have to print them on paper.
This was actually the main reason I didn't buy a printer.
I did this for my enviro sc 1A03 course, since it had blanks I had to fill in. What's really nice about OneNote is that it tries to simulate a real notebook with sections and tabs, keeping you organized all in one place. I suggest playing with it, if you're seriously considering using it so you're not scrambling about all its features during the year. I ended up buying my laptop early in grade 12 so I did a test run with my exercise science course and it worked really well.
Like everyone has mentioned already, it may be hard to type formulas in math, chem, physics, so you might not need this for every course. Though, you can opt to buy a more expensive computer with a touchscreen and use OneNote as your notebook. I imagine this works very well if you get used to it. And I have seen someone do this in physics.
To top it off, you can easily back up your notes by using dropbox. All you do is save your 'notebook' in the dropbox folder and it will back it up every time you made a change to your notes. Oh btw, you don't have to remember to save in OneNote, it does that for you pretty much every time you make a change.
I do not suggest using microsoft word because it's not very efficient. You have to remember to save it and you end up using a folder system instead of the much better notebook system in OneNote.