I have been veggie gardening on and off for many years now. I am an expert on the basics and easy veggies, but have not ventured into anything too difficult yet!
My favorite things to grow are greens.....salad greens, kale, spinach, chard, etc. Squashes are pretty easy as well!
I would love to get an inexpensive green house so we could grow during the winter months!
One book that I would recommend is 'The Secret Garden of Survival.' I like his ideas about how to grow things in a more 'natural' way, so it is hidden.
http://www.secretgardenofsurvival.com/
https://www.youtube.com/user/SurvivalistGardener
We have been gardening for 20+ years (but not an expert on anything) here in upstate NY. We too, have dairy goats (as well as chickens) and compost the barn cleanings for the garden.
We grow quite a variety of vegetables. The Lord impressed upon me a couple years ago that I need to learn how to harvest seed so I have been working on that end of it also. We grow all heirloom non-GMO plants and start all our seedlings at home. This avoids bringing unwanted disease to our garden plots.
Here is a great source for seed-
www.rareseeds.com