Congrats on moving to Madison! If you can give me more details on what you're looking for I can help you out w/a bunch of your questions. What type of homeschool group are you interested in? (Christian, secular, unschooling, coop, etc). There's several good groups in the area.
What kind of animals do you have? I breed German Shepherds & have a couple of vets that I really like but part of that depends on where you end up living.
Are you looking to buy or rent? How much acreage do you want? Do you have any preference as to area? Where is your job going to be located? I'm a Realtor w/Restaino in Madison so I'm sure I can point you in the right direction if you let me know what you're looking for.
Not sure about ballet but I have a family Dr who I really like. She's with GHC though, what insurance do you have? I used to be w/Dean & also had a family Dr there who was great. Both are on the east side though so that will also depend on where you end up living.