I'm writing this because I've received more bad packaging than good, and most of the good jobs could have been done for much less money.  As an occasional seller, I know the value of keeping cost down.

The most important part of shipping fragile items is padding.  The Post Office recommends at least 2" on all sides, & I think this is a bare minimum.  It's also the most frequently violated rule out there, and all too often the cause for denied insurance claims from the Post Office.  That's right, I said DENIED!  Just because a buyer gets insurance on a package doesn't mean the PO will pay up on a broken item.

I've had several claims denied in the last year due to "insufficient packing", which means that I then have to try to get my money back from the seller.  This is often contentious and always unpleasant.  Nobody wants to have to refund money, especially for valuable antiques.  When in doubt, get a bigger box!

Here is what I consider the best possible packing method, followed by a few suggestions to save costs:

1. If the item is hollow, like a vase, gently but firmly pack the inside.  You can use crumpled paper or plastic bags, foam peanuts, etc.  Odd bits of bubble wrap will also work here.  If you are shipping more than one item, nest them if possible, with plenty of padding in between.  If they clink when you put them together, use more padding.
2. Securely wrap the item with some kind of padded material.  This can be bubble wrap, tissue paper, newspaper, plastic bags, even old towels!  Just be sure that they have enough padding to be able to withstand a moderate impact.  If the piece has smaller protrusions, like the arms on a statue, pad those extra heavy.  Resist the urge to break up those molded Styrofoam forms that come with your latest electronics purchase.  While they can be useful (sometimes), they are also really, really messy!  If you don't believe me, try this:  In your living room, break off a couple pieces.  Now bash the broken ends against each other for 10 minutes or so, and then see how long it takes to clean it all up.  Those little Styrofoam nuggets will actively resist containment, flying away from even the strongest vacuum cleaner!  I usually use small lengths of tape I save when I unwrap an item, because once they're stuck. they are usually stuck for good.  Just be sure to fold the sticky sides against each other when you throw it away, because they have been known to still escape confinement otherwise.
3. Use only enough tape to ensure that the padding stays put.  This is the single biggest waste of money for most shippers.  You are trying to secure the padding, not mummify the item!  Also, if you are using bubble wrap, try to NOT tape the bubble side!  When I unwrap the item, I try to save the packing materials to reuse later, and most packing tapes will rip open the bubbles, rather than come away cleanly.  Believe it or not, ordinary Scotch tape works very well!  Duct tape should only be used on the outside of the box, if at all, and never directly on the item being shipped.  This is a case of the adhesive being too strong.  It's also more expensive than other tape.
4. Select a box at least 2" larger in ALL directions than the lump you are now holding, and put about 3" of padding in the bottom.  Now put the item in & cover with another 3" of packing.  When you close the box, it should all pack in nice & snug.  Before you tape the box closed, shake it gently.  If you feel or hear ANYTHING shifting around, add another inch or so of packing & try again.  Don't seal the box until nothing moves inside.  Just don't try to cram so much stuff in the box that you break what you are packing.
5. Now, select another sturdy, corrugated cardboard box larger that the first box.  If you can, another 2" bigger all around will be the best.  Repeat the packing process.  Even if the second box is just barely big enough to hold the first box, it will still add vital stiffness.

If you've followed these directions reasonable close, you now have a package that will resist virtually anything, and in the unlikely event some damage does happen, you won't be responsible.  With this good packing, all of the major shippers will cover any insured loss.  As a collector of pottery from a company that went out of business 40 years ago, I would rather pay for an extra pound or two of packing than see one more piece of the dwindling supply of good items get broken in transit.

That said, there is no reason you need to spend much, if any, money on packing supplies.  Crumpled newspaper is STILL one of the best packing materials ever created, and you can probably get all you need for free from your friends, family, & neighbors.  And while I am not recommending that you do this very often, emergency stocks of papers can be had from any of the numerous free publications that clutter the street corners in most cities.

Shredded paper should not be used unless you absolutely have to, because shredding actually REDUCES the cushioning value!  If it needs to be shredded, you shouldn't send it to a total stranger, and if it doesn't need to be shredded, it's just a waste of time.  I once received, as packing material, the contents of someone's office shredder.  After I re-assembled 2 old checks & sent them back to the seller, they got the point!

Foam peanuts also work great, but unless you either buy as many items from eBay as you sell, you will probably run out from time to time.  If you work in an office, you might be able to collect any that are received there, unless your company already does that themselves.  You might be able to get free bubble-wrap this way, as well.  The best type of peanut is the "green", environmentally friendly kind.  It doesn't wear out & shred like the Styrofoam ones do.

Bubble wrap really is the gold standard for packing material.  With enough layers of it, you could just about play football with a vase.  Unfortunately, "gold" is the operative word here.  I save & re-use all of the bubble wrap I get, even the bad stuff.  The worst thing you can do to bubble wrap is to tape the bubble side.  This all but guarantees torn or popped bubbles, leaving you with crappy plastic wrap.  When I get some in that way, I will just cut it off & save the lump to use as filling, either inside a hollow piece, or just in the box with whatever else I have.  It also works well to pad around little points & protrusions on things.

In closing, I would like to suggest that you NOT mix types of padding, if you can help it.  I, along with a growing number of others, believe in the saying "Reduce, Reuse, Recycle", and I get a little growly when I have to try to separate Styrofoam peanuts from shredded paper, or sit & fillet the tape away from the edges of the bubble wrap so I can try to save it.