Hi Lacey, the meaning is the same in each sentence. I would choose the third sentence - it puts "in principle" as a signpost for readers - a way to tell them that we have rule (there's no cost to use the library) but there will be some exceptions to that rule (so it might not be free in every situation). I hope that's helpful!

They are identical in meaning. I prefer them in this order: #3, #1, #2. Also, I think that #1 should use commas in this way: The public library shall, in principle, be free of charge.

Normally, we put "In principle, " at the beginning of a sentence for emphasis because it introduces a major limitation on what you are about to say. It means that you are about to say something that does NOT follow that principle. If you REALLY mean "to follow this principle", you should omit it. Or if you must state it, say something like "will follow the principle of free access to all".