You can easily compost straight grass clippings. I've done it for years. I finally got Castle Key doing it, too.
One of the most important tricks to composting all grass quickly, and without any nasty odors, is to turn it FREQUENTLY. Bacteria can quickly go anerobic in grass, and when that happens you get nasty methan odors, strong ammonia smells, and other unpleasant things.
Castle Key is using his for his garden, but what you can do with yours?
This fall, after the grass goes dormant, screen it and then spread it evenly over your lawn.
You will be rewarded in the spring.
If you want to get really ambitious, plug aerate the hell out of your lawn, then mix the grass compost 50/50 with leaf compost and rake it into the plugs.
You will be rewarded in the spring. IN SPADES. Especially if you put a cover layer of new grass seed over top.
Do NOT compost the dog poo with the grass if you want to use it on garden plants. Dogs eat a lot of meat, horses and cows don't. It does make a difference. You could always get a doggy doolie for your dog poo. Essentially it's an in ground septic system for your dog.
As for the wood chips, use those around trees or bushes. Don't try to compost them, they will take forever to break down. Give them to friends and family. Burn them in a fire pit.
Here's a description of how to make your own dog waste septic system.
http://www.plantea.com/dog-waste-compost.htm