I think either or both would be fine. The paper might have a tendency to blow away unless you add something on top of it.

I use pecan shells as mulch. They are not only a great mulch, often they cary bits of nuts in them that help add nutrients to the soil as well as having an acidifying iron adding effect. If you have access to pecan shells and have alkaline soil.. That's the ticket. Paper could go in the compost but is basicly nutrient free cellulose.

Tilled in the paper would not be mulch and would not do much to block weeds (although it might have other benefits depending on what you are planning to do with your soil and what your soil is like). I have successfully used shredded paper as mulch but it helps to wet it a bit or put something on it to weigh it down so it doesn't blow away. Sometimes the shredded paper can turn into something like paper mache which does not breathe as well (although the "paper mache" doesn't happen to have done much, if any, harm in my projects). Newspapers or cardboard are a little better as weed blockers than shredded paper but since you have shredded paper to use give it a try or use a combination of the options.

If there is a Starbucks on your way to work, I suggest stopping there and getting the coffee grounds on the way home. I do that daily and get about a cubic yard of grounds a month. Mix the paper shreddings with coffee grounds, moisten them to dampness and let them compost. Then use that as mulch.

I'll try doing that to see how fast my shredded paper and coffee grounds turns into compost.

Great ideas and we just had a Starbucks open here too. Thank you.