Greens can tolerate some shade, but they won't grow as fast. Fruiting vegetables usually need a lot of sun. They don't get a lot of sun, and you don't get a lot of fruit. Lack of sun is going to be a major problem, especially in a cool climate.

No fence? Keeping deer out will basically be impossible. Smaller pests can be dealt with, to some extent, with traps. Scary stuff (sights, sounds, smells) may work partially.

Books have been written on the questions that you ask. Your best online option, and the best place to start, is your local extension service, which is here

https://www.canr.msu.edu/home_gardening/vegetables/

For low growing plants low tunnels are effective against deer. With your shade situation you can grow greens like dan said. Onions can also be grown. I have a similar problem with shade and resorted to container growing tomatoes on the porch and deck which get much more sun than the ground level. I try to get started early with the garden before the trees have much in the way of leaves. I recommend starting seeds indoors.

That's a good point about tunnels. I kinda regard those as fences, but they are much more affordable. They could also extend your growing season, which will be an issue up north. That being said, they can be pretty inconvenient.

define woods - how dense? as the woods i'm familiar with get zero direct sunlight except some filtered light. there must be a spot that gets some direct sunlight for a few hours or it will be a waste of time, unless all you plan on growing are baby greens. is there any current vegetation growing? (grass, weeds, etc?) if no, then unlikely not worth spending much effort setting up garden.. maybe try planting some lettuce in some pots as an experiment before investing time.

Shade is the enemy of a good vegetable garden. Six hours of sun is a minimum. Some herbs tolerate shade though. You can make a fairly inexpensive and low profile deer fence using the plastic fencing material and metal stakes, sold in most hardware and lawn and garden stores. Smaller animals don't like to climb wobbly fences . . . Groundhogs will be another issue though, and the smaller animals will chew through plastic. Chicken wire also could work for both small animals and deer. That's what I have used. If it were me, I'd focus mostly on herbs like mint, thyme, oregano, maybe parsley . . . lettuces. Grow sun loving tomatoes, basil and pepper in pots and season your dishes with the herbs.