So are you just buying boxes of trading cards and hoping they will be special ones inside.
Basically, yes. You won't know what's inside the box until you open it. You could pull a couple of high-numbered, common inserts that sell for $10 or less on eBay, a rare or variant insert, or anything in between. It's a lot like gambling.
You'll need to do some research before buying a box. If you want the chance to pull inserts, you'll have to make sure you're buying a hobby box. They are more expensive than retail boxes, but you can spot them by reading the info on the box -- it'll state whether there are autos, costumes and props inside. If in doubt, always ask the shop owner or eBay seller if the box is a hobby box. The link you posted is for retail packs of POA that were produced by Cards Inc. (they had permission from Artbox). Those packs have only base and foil cards. Artbox also produced its own retail version of the set, again without inserts. The hobby boxes for POA are very expensive because only 5000 were produced and it was the first HP set with inserts. They're quite scarce now.
Another company, Wizards of the Coast, produced a Sorcerer's Stone set before Artbox got the license. It has only a base set.
My guess is that the lowest box prices you'll find are with the two upcoming releases. You could try pre-ordering a box or two and see how it goes. You can also check with local shops and online to see if there are decent prices for previous releases.
It's a lot of fun to open boxes, but it's been my experience that in financial terms, people are better off buying the individual cards they want. I've spent $55 plus shipping for a box that contained less than $25 worth of cards, while others have pulled a Dan auto or variant prop from a box. Of course, if you don't buy a box, you have no chance of pulling that Dan auto.