Any chalice that does NOT have the word “root” in it is pre-designed by the devs, so when anyone makes a dungeon with those chalices, it’s the same for everyone. Any chalice that does have the word “root” in it is going to be randomly generated. In the former, most rewards and pickups will just be materials or whatever to make lower “depth” dungeons. Essentially, those are progression dungeons. You’ll want to do just about all of them because in most cases completing one also gives you access to a new “root” chalice. So for the latter, the root chalices, you’ll basically use those to search for good loot such as high level blood gems or runes.
“Depth” refers to general difficulty. 1 is like early game, 2 is like mid game, 3 is like end game, 4 is like NG+, and 5 is like NG++. Just approximations.
Later chalices will require more materials to be gathered, but normally for most of the non-root ones, you’ll get enough just be completing previous chalice dungeons you unlock. However, once you use any chalice once, you can search for dungeons other players have created using that same chalice, and load it up without paying material costs. So, about that, you can share any dungeon, root or not with any player by sharing the glyph code of the dungeon, which you can examine after placing a chalice on an altar. By doing this, you essentially only have to pay the material cost to use a chalice once, because every time after you could just enter someone else’s. Still, in the case of a root chalice you may want to roll your own dungeon anyway if you haven’t found any good gems or runes in other peoples.
I guess to summarize, do all the ones that don’t have the word “root” in them in order to unlock all of the basics. Then, do “root” dungeons at lower depths to gain loot, mostly better gems and runes, and sometimes also alternate versions of weapons which just have different gem slots.