I have both NDs (Nigerian Dwarfs) and Alpines. My NDs are only six months old and just like little puppies. They follow me everywhere, love to get hugs and be on my lap and on the car and on the picnic table and on anything else they can get up to, and constantly try to sneak into the house. If we're outside working, they are literally under our feet. I learned real quickly to never muck stalls with them running loose. As soon as I get the wheelbarrow filled up, one of them jumps into it and tips it forward and all the poop falls out ... and I start over!
I milk my Alpines. They were two years old when I got them and are very, very sweet. They love to wander around but stay pretty close to where we are when they are loose. I actually don't let them out of their fencing very often though, it changes the taste of their milk.
You need to spend some more time deciding what breed(s) you want and then start looking for someone in your area that has that breed. You can watch craigslist (be careful of unscrupulous people), local feed stores, country vets, etc.
Goats aren't good lawn mowers as already mentioned. They are browsers and will take out your small trees, flowers and shrubs. (I agree, if you want more of a lawn mower - get sheep.)
Goats do really well in a small shelter that has a small, low door. Depending on the severity of your winters a three sided shelter can work. But, if you have snow or cold, windy days they would be healthier in a four sided shelter with the small door.
Fencing is everything with goats. If the fence can't hold water... it can't hold goats! Well, it sure seems that way..
Good luck and have lots of fun with your new adventure.
