To get all the weapon upgrade trophies you need:
hardstone, sharpstone, clearstone, greystone, bladestone, dragonstone, suckerstone, mercurystone, marrowstone, moonlightstone, darkmoonstone, faintstone, spiderstone, and cloudstone
For hardstone / sharpstone you will need 40-55 shards, 23-29 large shards, 11-14 chunks, and 1 pure. For the rest you will need 15-20 shards, 6-8 chunks, and 1 pure per weapon, and also however many hardstone or sharpstone shards it takes to get the weapon to the required starting level of +3 or +6 in order to set it down one of the other upgrade paths. If all you care about is the trophy, and not actually using the weapon, then pick the weakest weapon available to upgrade. The crappier the weapon, the fewer stones it takes to upgrade. This has a list of all the stones, and a list of all the weapons which can upgrade with that stone. On that weapon's page it will tell you how many stones it takes.
http://demonssouls.wikidot.com/upgrade
Shards and large shards of all ores are usually either purchasable or easily farmable, so feel free to go nuts upgrading as long as you stop upgrading before it requires chunks unless you plan on sticking with that weapon for awhile. Chunks are typically more time intensive to farm, and some pures aren't farmable at all.
http://demonssouls.wikidot.com/stone-farming
My character that has most of the trophy related stuff is too high for you to coop with, I am not sure what items are on my lower level characters.