To me, a proper Libertarian has the basic principle of "government is for internal order and external defense, and not for interference in personal lives or business unless force is already being initiated by other parties", and looks at these things through both a lens of practicality (what works in theory doesn't always work in practice) and a lens of "rational *LONG TERM* interest" (I emphasize "long-term" because it's often a forgotten principle); in addition, a rational Libertarian recognizes that they are part of a larger society, and that the benefits of this powerful and advanced civilization are based on the continuing coordinated work of literally millions upon millions of people who do not -- and WILL NOT -- share all of your views, and some of whom may have almost directly opposing views, and who STILL have to all work together as part of the society, if not as friends and family.
Similarly, they must recognize that the basic principles of the society include the fact that we don't let people die if we can help it, even if they do stupid stuff or get themselves in a predicament through laziness, and that the basic laws of humanity mean that some significant number of people are lazy, dishonest, or downright criminal... and won't necessarily get caught.
Putting all this together, a sensible Libertarian should arrive at the following conclusions:
1) Taxes, while morally reprehensible in the abstract -- amounting to giving the government a license to rob -- are one mechanism to assure payment for services that the government is legitimately expected to provide (internal order, external defense). Some form of nonvoluntary funding, at some level, is going to be inevitably necessary in a large society to avoid the consequences of the Prisoner's Dilemma/Free Rider problem.
2) It is in my best long-term interests to maximize the functionality of my society so long as it does not UNDULY cost me in some other area. The "Unduly" is a matter of judgment, of course, but it should be recognized that unless I am myself sufficient unto all things, and still wish to maintain my modern-life lifestyle, I need to accept that there will be -- and must be -- some cost to my rugged individualism in this.
3) Costs to save lives rise rather predictably with the seriousness of the condition from which the person is to be saved, and the extent of work needed to be done to abate the condition. Some acute serious conditions (drowning) can be addressed quickly and relatively cheaply, but in most cases not.
4) Since the society to which I belong values all lives at least to the extent of not allowing deaths to occur when preventable, and since those who cannot or will not pay will therefore be saved at society's expense, it is in my best long-term interest to take actions to minimize those costs -- and preferably all other medical costs, since reduction in medical costs will free up resources for uses other than just keeping people alive.
5) The best way of minimizing health costs is to treat conditions as soon as possible and prevent conditions whenever this is practical. This requires regular checkups and the ability of any citizen to get care for any condition as soon as it is noticed.
6) This is, by its nature, not a profitable business. Overall such care will cost more for any individual group providing it than can be recovered by ordinary means (free riders, the incapable, the broke, etc.)
7) As this is to benefit all of society, and will contribute by its very nature to internal order, the strength of the nation as a whole, and in the long term my overall prospects, this is therefore a legitimate function of government -- assuring all its citizens of access to the health care that they expect from the most advanced civilization on the planet.
From this, I obviously favor a universal health plan -- one whose operation is basically like New York State's Child Health Plus or better. In essence, anyone below a particular -- quite reasonable -- cutoff pays nothing, those above pay a graduated amount per month, up to a cap which is still quite affordable for the salary level at which it applies. No copay, no deductible, covers everything short of plastic surgery for cosmetic purposes (and I'm not entirely sure about that).
This would require a number of major overhauls to the current system; protect doctors from current malpractice costs (my father in law was paying something like $100,000 PER YEAR for such insurance... and as far as I know he was never actually sued, so that wasn't due to some terrible oopsies on his part), reduce expectations of perfection (doctors can err), set standard fees for known services (adjusted by regional costs -- the GSA already does this for other things), and of course that'd be the death of health insurance companies. To get it passed, you'd probably have to -- speaking perfectly bluntly -- bribe the companies. Pay large sums to all the major players, and guarantee pensions to all the long-term employees so that you didn't kill off a few hundred thousand careers just like that. Long-term cost on that part would be trivial.
It would also in the long run save us a lot of money. All arguments to the contrary, we have had one of the most costly healthcare ... setups, for "system" implies something unified, which ours was not... in the world. It is, in fact, the best -- when you can afford the best. It's also one of the WORST in the civilized world if you CAN'T afford to pay. And it's been steadily getting more expensive. Part of this comes from the "take care of everyone" interacting with "doctors charge as they want" and with "insurance companies need to make profits" and "we want perfect health care with our insurance" and "if the doctor makes a mistake, sue!"; combine them and you have a recipe for constantly increasing costs all around, each increasing the next and the next causing its neighbor to increase in turn.
Having lots and lots of people who are afraid to go to a doctor because they can't afford it means they don't go until they HAVE to... and by then it'll likely cost ten times as much. They'll be out of work for weeks instead of a day or two, which impacts the employer and his customers. If they can't pay, that's ten times the cost charged to society (because we won't let people die). You can't avoid these costs unless you either (A) make damn sure everyone's cared for, or (B) are willing to let anyone who can't afford it die or suffer. This is not the general way America looks at itself, so (A) is the only reasonable, rational, and acceptable alternative. In the long run, it's also a sensible, cost-effective choice... IF, and ONLY IF, you can get it enacted that way.
Compromising on it, however, will screw everyone -- in the long term, even the insurance companies and/or the people running them. Companies, however, live on the short term -- this quarter, this year, maybe five years... but not twenty, thirty, forty years. And that's the timeframe any of us should be looking at.
I'm running out of time on this; later I have to talk about other parts of my current philosophy, like why people are afraid to let their kids play outside when its safer today than it was when I was a kid...