Absolutely mulch in the fall. For most of us that is when we have the most material readily available and that mulch will help protect your soil from winter erosion. As long as you do not make the newspaper layers too thick, I've found that 5 to 6 pages are about all that is necessary although for places I do not plan on a future planting I will use more, the soil bacteria will most likely have most of it digested even before snow fall, if you have that.
For a cover use what you can get the most of for free.

I've noticed good improvement in soil with layering ~5-6" of leaf muclh over beds. The worms appreciate it and the soil is more friable in spring. Coarse straw is fine, but unless you rake it in, it won't break down and provide nutrients as quickly as leaves.

I would use the leaf mulch because as much as some folks say there are no seeds in straw vs hay, there are still seeds remaining and you will curse them come the spring!

I now hot compost all straw/hay for that reason. Never use it as mulch when you have something else available.

Ive used straw as a mulch for several years now, and it did well. Had a lot of wheat for the compost the following spring. This year, Im going to try cover crops and see if I get better results next spring. I have heavy clay (improving tho), and last year was awful cause I covered the garden to much. The soil was actually worse than better.

Nah! Don't worry about the paper. IN the spring most will have decomposed. Just rake away where you want to plant and then put back the mulch when the plants are big enough to withstand slugs. I sprinkle dried eggshells around my plants to keep the cutworms and slugs at bay.

Mike, If you have soil that doesn't dry well in the spring and you cover it with mulch, it may not dry till July. In my first year of gardening I covered my heavy clay soil with 6" of leaf in the fall. In the spring I had a heavy mat of wet leaves covering my garden and still had mud when all my neighbors (who didn't mulch) were planted. I ended up raking the mess off the garden and letting it dry. Live and learn.
If you have a fast draining soil and dry springs, mulch to your hearts content. If you have a heavy clay soil or wet springs, I would try several different types of mulch to get a feel for how my soil would react to them.
The past two years I've been using a year round straw mulch, and when planting time approaches I've raked back the straw in the areas that I direct sow in. It allows the soil to dry and warm up. What ever you do, be prepared to rake.
No two years are the same. It's all one big experment. Enjoy.
Dan

People with sick soil will see problems when they mulch with the leaves from their trees in the fall the following spring as Dan did, but over time (the soil did not get that bad overnight and it can't be cured over night) it will get better. Those that have lots of leaves each fall should never, ever rake them up, bag them up, and throw them away because leaves are just too valuable to do that with.
1) Mulch mow those leaves back in the turf, so the nutrients they hold feed the soil where they came from.
2) Pick them up with your mulching mower and use as mulch on your planting beds.
3) Never, ever rake your turf grass since that damages the grass crown so it does not grow properly.
4) Never, ever allow any "yard waste" from your property to leave, always recycle any of your yard waste on site.

I use either. This fall I've been putting straw through a shredder to make it finer so it will break down faster. When I use it unshredded, I have some of it stick around for a couple of years. I can put straw on thicker than leaves, because the leaves mat too much, but they're the big leaf maple leaves, so yours may be smaller and not do that as much.