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You're actually asking more questions than you think here.
1)  Your farm does not get USDA approved.  You go to a butcher who has a USDA inspector on staff to inspect the meat as it's slaughtered.  
2)  In order to sell your meat retail, by the cut, to a store or restaurant, etc. it must also have approved labeling.  This includes the safe handling instructions and USDA logo which all meat at the supermarket has.  You have two options:
a)  If your butcher is USDA inspected, it is very likely they have a "house label" which is USDA approved already.  So they would package your meat, in their label, then you would be allowed to sell retail.
b)  You can get your own USDA labeling approved.  It's free.  It's just time consuming and most people limp by using the butcher's house labeling.
3)  If you are only selling whole/half animals to customers, "on the hoof" it's called, then you can bypass the USDA system and use farm butchers.  These are the mobile guys who come around.  The quality varies greatly.  Again this exemption is only if you're selling whole/half animals.
4)  Poultry does not fall under USDA inspection unless the facility processes over 19,999 birds per year.  This means that we have 50 different rules for 50 different states on how poultry (and rabbits) must be slaughtered and handled.
5)  Your facility does not get USDA inspected if you are selling your USDA inspected meat out of your freezer.  How and where you store your meat for sale falls under state inspection (we have to keep ours in a freezer separate from our domestic food supply).  Your County may also have rules for handling and storage.  The third thing is if you sell at a Farmer's Market, your state or county may have rules about how it is stored and handled.  In our County we can do it out of a cooler with ice, whereas next County over it must be in a mechanical freezer.
6)  The only time your facility would be USDA inspected would be if you wanted to start doing your own slaughtering and selling retail (in the case of cows, lambs, pigs, etc.).  If you want to slaughter and sell your own poultry, it's likely only a State inspection you will need.  Honestly, for all the trouble, I would just find a USDA processor and a poultry processor and leave it to them.
7)  Dairy falls under USDA and State regulations.  I won't venture to guess how your state works.  In ours (Washington), it is feasible to get a raw goat milk dairy approved on your farm for sale of milk.  Once you start making chese, though, you are a processor, then you're going through a whole other thing.
In general, you can do no work, processing or cleaing of anything within your own house which will be sold to the public.  So, you at some point will probably need a commercial kitchen (which would be state and county inspected) if you wanted to bottle milk for sale.  Just freezing a chicken you slaughter yourself is considered processing, so you must have all the permits in place.
The biggest issue I have found is finding USDA facilities that will even talk to you.  Most just slaughter animals under contract for the big grocery chains.  The ones are few and far between which specalized in custom meats like we do.  I haul my animals about 100 miles, and I'm far luckier in terms of mileage than some farmers I know.