What you are asking is a very large philosophical question.
I do not understand why your groups are mutually exclusive. I identify with both.
My personal definition of liberty is right along the same lines as Justice Oliver Wendell Holmes, Jr.: "The right to swing my fist, ends where another man's nose begins." Which is to say, if I am not hurting anyone but myself, and I am willing to personally pay the consequences of hurting myself, then it's okay. In other words, your group one.
However, many, many generations of philosophical thought have gone into what a government DOES and SHOULD do. From hereditary clan chieftans to elected government officials, the main point has been that a government's responsiblity is to look out for the interests of its people, whether they be subjects or citizens. In other words, to ensure that the fist-swinging doesn't hurt anyone. Part of looking out the the interests of the people, is creating a baseline living standard. And that baseline standard is, basically, defining the metaphorical "nose." (You are free to walk down the street without being wantonly murdered, for instance, IS a baseline living standard. Ask anyone from a country where they are afraid to walk down the street.) I agree with that belief, that government should care for its people, so that also puts me in your group 2.
See? Not mutually exclusive.
The real trouble, as I see it, is defining where injury begins. In other words, where does your nose start? To take something a little less controversial, and slightly more cut-and-dried than the birth control or abortion debate, let's consider seat belt laws. You have to wear a seat belt. Why? Because medicaid and medicare recipients who are injured in car accidents harm the pocketbook of taxpayers. Because health insurance premiums for groups go up when there is a higher percentage of injured persons in the group. Because as vehicles are more widely used, an influx of severely injured persons overloads emergency rooms, delaying care for others. Because if the primary breadwinner of a family gets him(her)self killed, the family becomes someone else's burden. And so on...see? You could modify seat belt laws, to say that if you are injured in such a way that wearing a seat belt could have prevented the injury, then insurance or government assistance is not required to pay for your coverage, however, that would lead to a potential increase in disabled, destitute individuals, and that's just another nose. If you could word it in such a way to eliminate noses, well then, by all means, I am all for letting people skip seatbelts. I often find them uncomfortable, myself.
So the main problem, simplified, and really the only source of any debate over government - is if this decisions is preventing harm to others. If it does, fine. If not, then government has no reason to regulate it. The problem all goes back to defining the nose.