Many of us do not use wood chips as mulch in our vegetable gardens because it is too easy to get them mixed into the soil. Attempting to sift the wood chips to seperate sizes may be much more labor intensive than you might wish.
I'd find something less carbon intense to use to mulch the vegetables.

http://www.organicgardening.com/learn-and-grow/mulch

If you are going to compost a deer above ground, wood chips are essential. And wood chips are nice for walkways, especially when free.

I used some wood chips and smaller branches last year for making a German Mound.

But generally I avoid wood chips, and use materials that break down quicker, such as leaves and shredded leaves. Leaves are such a wonderful 'brown' or carbon-rich compost ingredient that I seldom use anything else. Paper seems like empty calories in comparison. A nice mix of shredded leaves with grass/coffee grounds/fruit and veggie wastes will heat up to a core temp of 150t 165F in three days.

October is my favorite month.

What about hay? I have been reading that a lot of people use it instead of the wood chips.

The easiest way to use them would be to put a thick layer in the path areas, and let them break down in place.

After they have time to break down, you move your beds over. The areas that were formerly beds get a new load of woodchips and become the path. The areas that were formerly path become beds.

If you spot a local tree trimming crew, those shredded up branches they end up with as a waste product from trimming trees are even richer than wood chips once they compost.

As a bonus, tree trimming crews give their stuff away since you're saving them a trip to the dump and paying a dumping fee.

Here is a link that might be useful: Using shredded branches to make good soil.

I couldn't recommend woodchips more.. Watch the link below, there is a free video in the right of the page, it will answer all your questions. This man moved to house and depended on drilling a well to irrigate his garden, end up the well eater was bot adequate for irrigating his garden.. He then looked in nature and noticed that natures ground(woods,forest,fields,etc) always had a mulch on it, whether it was living plant, or leaves, etc, natures soil is never bare... So he got loads of woodchips an leaves delivered to his house... Tree services normally pay to dispose of wood chips, they will usually happily give them to you for free... So he mulched his garden with a thick layer of woodchips and went from there... Now, he doesn't even water his garden what so ever.... I would also grow a cover crop if you can... Check out this video, it will help you enormously..

Good luck,
Joe

Here is a link that might be useful: Back To Eden