from the main view of your fort you can press l (small L) to see a list of all your legendary artifacts, and from there use the arrows to select one, and then press enter to have a look at it. the value of the item shows up in the top right, the weight in the top left. you can also see if its covered in blood, vomit, water, and who owns it. pressing k and selecting an item lying on the ground will also show you this. from this screen you press v to view the item in detail, which shows you the description and any images on it.
ive played for ages, and yes, the majority of artifacts are somewhat lame. as i think has been mentioned in this thread you can try and influence what gets made by training all your peasants and farmers up to dabbling skills like weaponscrafting, and you can store your most valuable/useful materials like diamonds, dyed cave spider silk and adamantium as close as possible to your workshops. moody dwarves tend to grab the nearest thing that meets their needs, so for metal bars any old bars will do, and for a gem your moody dwarf regards a cheap black onyx is as good as a saphire. remember dwarves dont understand distance in terms of z levels, a stored item one tile over is still only one tile over to them, even if its 40 z levels down.
ive taken to locking a dwarf in his shop when he first claims it, noting his list of demands, and dumping them through a hole in the roof to make sure he uses the best stuff possible. this is a lot of micro, but i would hate to finally get a weaponscrafter go fey and get a bronze axe when i have so much adamantium lying around. you can also check what they have stockpiled in a shop using t, and forbid anything you dont like. if they havent started construction yet they just go and find an equivalent material. doing this too much may delay them to the point they go crazy, so be careful. and remember the first item they grab will be the base material, and the rest decorations. masons can be coaxed into using valuable metal ores as a base material.
best artifact so far using this method was an adamantium crown with faint yellow diamond, red GCS silk, gold, platinum and goblin bone. with an image of itself on it.
and to the people wondering, you can buy gems from the traders and have been able to for the last few versions if their parent civ has access to them. same as flux stone. my dwarven caravans never have access to flux stone