How much land do I need?
Not a lot - we have 5-8 goats in a 1/2 acre area and it works well.
And, would my goats enjoy a partially wooded area, since most of my property is woods? Yes they love to browse, but expect the wooded area to get cleared out pretty quickly.
What do I do to winterize my goats in southeastern PA?
Just basic shelter to get out of the wind, they are hearty animals. A 4'x4' 3-sided lean-to is fine for a couple goats.
Are goats good with kids? Mine are 6 and 1. Generally, yes they are. Does or whethers are not usually aggressive and usually very friendly and like attention. It's best if you buy bottle-fed kids, they will be much more human-friendly. Kids raised with little human intervention can be skittish. For interaction with small kids, the smaller goats would be better, the large breeds can be over 100lbs and could injure a small child accidentally.
If I do not have desire for milk, can I get virgin goats and keep them from producing milk? Like any mammal a goat only has milk after giving birth and only for a short time - less than a year. You can get a doe who has had kids and she won't have milk agian unless you breed her.
Will my wife kick my rear when I come home and surprise her with my new goats? No Comment!
Do goats have the right personality to be yard companions, or are they victims of generations of being told that they are nothing but livestock? See previous comment about bottle raised kids.
Will they get along with my cats? Never had cats with ours but don't see why it would be a problem.
Other considerations:
Fencing - you need good fencing. Goats have a reputation as escape artists. We have never had an escape, but we did spend money on good fencing. You'll want 48" woven wire or 5-wire high-tensile electric. I suggest putting an electric strand over the woven wire to prevent them rubbing on it and stretching the fabric.
Health - the primary concerns will be hoof care and parasite management. Trim hoofs every couple months, monitor parasite load by having a fecal run and worm as appropriate. There are a couple of diseases to watch out for, the most important is CAE which causes crippling arthritis, make *SURE* your kids pet goats come from a CAE-free herd (see testing paperwork) or you'll be in for heartbreak in a couple years when the have to be put down.