The crafted instruments last for only three days, but so do the ones from the music box. You have to unseal them to use them. There is a 7 day version that was offered via the item shop. As for just storing the sealed ones from the magic box, that is really no different than just storing the mats to craft them.
The price of the mats for the crafted ones are about 1/3 the price of the the musical instrument box. And then considering that the music box is random, I recommend getting the crafted ones. Get your skill up to level 33 and buy or gather the mats.
As for the instruments:
rattle-good as it increases both defenses. But it takes one of the 40 buff limits, that and I am just too lazy to go make it.
lute-physical attack speed increase. does not stack with guitar
guitar-spellcasting speed increase. does not stack with lute
tambo-both damage increase
sax-reduces enemy damage. utter worthless. Requires to be with a range of 150 of enemy and 5 sec cast time.
All are party buffs, range of 150, 5 sec cast time, share a 2 min cd, and do stack with most stuff. Iirc there are three different speed buffs that the lute and guitar do not stack with, but sry idr exactly which ones. I want to say they are the lute and guitar, the s/p spiritual leader, and some speed pot.