Short answer:
You have to subtract your racial HD from your total levels because they are effectively like taking levels in a class. Therefore you can only take 6 levels of classes with this race. Your base attack would be +9/+4 if you take those levels in ranger and barbarian.
Long answer:
Well, I see a small problem with your build. If the other members of your party are 10th level, then you should be as well. The thing about your race is that you recieve 3HD and 1LA (of stats and abilites). This is effectively 4 levels of classes that you "lose" for being this race. What we call this is ECL (effective character level). You add all racial HD (3), LA (1), and class levels together to find your effective level. So if you are making a tenth level character, you will have to submit 4 of them to your race (3 for HD and 1 for LA). Therefore, you can only have 6 levels of classes to be ECL 10 with this race.
As for your base attack question: You get +3 for the 3HD of Goatfolk (monstrous humanoid if you want to be technical) and +x for however many you get from the classes you take (if all 6 are in Barbarian or Ranger, you will get all 6. This would make your base attack bonus +9/+4).
As you can see, you really only lose one base attack for being goatfolk (for the level adjustment level you had to take) since you get good base attack with the monstrous humanoid hit dice it makes you take.