A libertarian system isn't necessarily based on property rights- it's based on individual freedom, and particularly freedom from coercion*. Most libertarians, however, do also believe in strong personal property rights, and it's well arguable that ones ability to exercise ones freedom depends a lot on how much property you have, insofar as property is a determiner of wealth (possibly the determiner of wealth, depending on your definitions).
This brings up another important point- in a libertarian system, your power is determined by your real wealth, not by how much money you have. Money is only one contributor to wealth, although it's a particularly convenient and easy-to-track one, and so often gets mistaken for the real thing. (Of course, even if money were power, it's not necessarily any worse than the current situation.) Other contributions to your net real wealth include property you already own, your time and capacity to perform labor (especially important as it allows you generate more wealth), contracts that give you rights with regard to anyone else's labor or property, even your reputation, etc. It's true that any property rights that you may want but do not currently control can be denied to you by their owner- but that works both ways. It's the basis for negotiation which underlies a market economy.
*C-Dawg tells me that that is based on a property right- the right to control your own body. Not sure what to think about that. It's an interesting point that just might be correct.