Congratulations on your plan! It is totally doable, and it sounds like the right thing for your family. We are currently living that same scenario -- small homestead farm, one working spouse, and one spouse home with the kids. We love it and would not trade it for anything. The privacy, the self-sufficiency, the nature -- priceless. Upstate NY is fabulous -- we lived there for many years.
First piece of advice -- subscribe to Mother Earth News magazine. It's everything you need. They are also online, and in their archive they have 40 years of articles on: gardening, energy efficiency, raising chickens and other animals, beekeeping, preserving food, tools/equipment, and on and on. If you encounter a question at your new place, I guarantee that ME News has written about it. Grit magazine is also good, but geared a bit more toward the larger farm, with 4-legged livestock.
Chickens are easy and super fun. For the basics look at one of the two publications above, but you will also just figure it out as you go. Your wife and kids will love it. The most important thing chickens need is a good coop that protects them at night from predators. Building a good coop will take you some time, but once it's done right it's done for many years. It needs to be dry and well ventilated, but not drafty. (Chicken's feathers are super insulating, but only in still air). Keep in mind that some predators are small (snakes and weasels), and some can dig. You need to use hardware cloth in your coop build to keep all those guys out; chicken wire doesn't cut it. If you are interested in egg layers that will also be good, healthy pets, I'd suggest you stay away from hybrid egg-laying types. They have been bred only for egg production, and suffer from more health problems and a shorter life span than a good heritage breed. Check out backyardchickens.com or -- again -- one of the above publications for an overview of good homestead breeds. Finally, you'll need to decide whether to free range the girls, or fence them in. The more freedom they have, the better their life will be, but the more predator danger. We have a fenced 1-acre pasture for our 11 chickens, and for us that strikes the right balance. The fence keeps out dogs, and although the chickens are still vulnerable to hawks, they have a great life. We have a patch of woods and lots of bushes in the pasture, so they are able to dive for cover when they need to. In the past year and a half at this location we have not yet lost a chicken.
Bees are a labor of love. I have been teetering on the verge of starting beekeeping, but have not yet taken the plunge. I know beekeepers for whom it is cost effective and the honey provides a nice cash crop. I know others who lose money on it but keep doing it year after year because they feel it's important. I'd recommend that you not start on beekeeping until you have gardening, chickens, and the basic property management humming along. Then take a class at your local cooperative extension. Very informative.
Equipment. For mowing, your needs will depend on the property you buy -- How much do you need/want to mow? Is it hilly or fairly flat? Do you plan to also plow earth or snow with the tractor? Any other things the tractor will need to do? I would wait on making any tractor decision until you have the property and have some tentative answers to the above. Keep in mind that a 4WD pickup can do much tractor work. (We have an old one that we use to pull stumps, drag logs, etc. as well as hauling loads. ) Ditto on major tools -- I would take it slow and see what your property needs. And check Craigs List for used tools/equipment. For our woods management, some of the things we use all the time are: chainsaw, pruning saw, lopper, tree trimmer, axe, maul. For the garden: wheelbarrow or 4-wheel utility cart, shovels, broadfork, hand trowels, rototiller (wait on that one until you know exactly how much you are tilling, and whether your tractor will do it).
Big picture:
*Check the fracking/power line situation for any property you are looking at.
*If you don't homeschool, be sure to check out the school district.
*Figure out how far the property is to the nearest grocery and hardware store.
*Check internet and cell connectivity.
*If you are interested in making your new place energy-efficient, look carefully at how the house is situated with regard to the sun.
*Look at the potential gardening spots with the same eye -- how does the sun travel over them, how many hours per day do they get?
**Taste the tap water in the house.
*Examine the house critically, and go into it clear-eyed about the work that will need to be done on it, and whether you and your wife will have time to do it. You'll both develop the skills you need, but do you have the time and inclination to do it? If not, how much will it cost to hire it done?
*Finally, try to visit some folks that are living the small-farm life. You'll learn a ton.
Long post, hopefully helpful. Feel free to PM me as well.