Well, a private tutor for sure would help. I think you should take the group classes and the private tutor. If you can only take one, then I would say that the group classes are better due to the Japan related events and because you have more people around you to study Japanese with.
In my own opinion, I think this site is kind of like a big private tutor. Again, in my opinion, private tutors are there for more of your language-specific questions.
For example, the majority of this site asks questions about more advanced Japanese. And if you have a private tutor then I think you will get the most out of him/her if you ask the advanced questions. I'm positive your private tutor would help you learn Hiragana, how to make simple sentences,etc., but that's all things you can easily learn on your own(depending on how difficult you find it).
So, if possible, have group classes and a private tutor. But if you can choose only one, I would go with the group classes ^_^