cover crop for backyard garden

I'm looking for recommendations for a cover crop for my vegetable garden (apx 1000 sqft). I'm in zone 5 and have never used a cover crop so I'm not sure where to even start! Here are some considerations:
-has to be an annual
-would like to plant the cover crop after double digging and amending soil in the beds this spring (I plan on doing the double dig one time and strictly mulching after)
-it needs to be easily chopped down so I can plant in the beds later this spring and summer. I'm thinking of just clearing where I plant though and leaving the cover crop between the plants (does this seem like the best idea?)
-I'm hoping to get a load of wood chips later in the summer/early fall to do a more permanent mulch, so I'd like the cover crop to be high in nitrogen to help off set any nitrogen the wood chips will take.

With these considerations, what recommendations for types of cover crop do you all have?
Thanks!

Hau, Sarah, I like buckwheat for cover cropping vegetable gardens also white or scarlet clover are really good. The best cover crop however would be a mix of buckwheat, clovers, hairy vetch, winter peas. plant these and chop them before planting season gets here.
I am pro "keep the soil covered" so I don't really have any areas of gardens that are monoculture. I keep "weeds" cut short but don't pull them, If there is bare soil I put in something low growing to keep the soil covered, there are lots of things you can plant between your crop plants that will grow with a beneficial role to the crop plants. It is also a good method to think "Three Sisters" when planting any garden. You just have to discover the plants that like to grow together like the traditional corn squash bean/pea combination.

I totally agree with and encourage your idea of planting within the cover crop/s.

If you are going to go to the trouble of double digging a garden bed, be sure to add Biochar as you are doing the dig, it will give long term benefits of many types. Check out this site for information Biochar International

I use dutch clover (fixes nitrogen) and daikon radish dies in the winter leaving a nice 2ft deep hole in the ground for you next plant grow into. Daikon radish root also goes down 7ft mining minerals and bringing them to the top.

For a quick growth in the spring, I would go with what Bryant suggested, the mix of buckwheat, clover, vetch..

In my experience vetch is going to be the easiest one of those to deal with. Buckwheat and rye make some pretty impressive roots and clover is incredibly persistent. I love clover but I don't if I can advocate it as a cover crop simply because it can be very persistent. So you might not be able to get rid of it completely if the time comes where you want to.

At risk of being crucified by some of the farmers here; I love chickweed. Chickweed is a great cover crop.

Edit:

If you are planning on sheet mulching heavily you can get away with just about anything. Clover included.