In Majora's Mask, there are 5 things that can be upgraded, sword, shield, bomb bag, quiver, and wallet. The bomb bag and the quiver, you start the game not having at all and the other 3 things, you start off with the lowest version of.
You start the game with the kokiri sword with an attack strength of 1. As long as there's no ice block over the hearth in the building in mountain village, you can give them the kokiri sword on day 1 or day 2 and they will give convert it into a razor sword with an attack strangth of 2 and give it to you if you talk to them after the dawn of the next day. The ice block is always gone in the spring but you can also make it be gone in the winter by either using a fire arrow or hot spring water. Once you strike with the razor sword 100 times, it turns back into a kokiri sword. Playing the Song of Time also turns the razor sword back into a kokiri sword. If you talk to them again on the second day when you have the razor sword, they will ask you if you want to make it even stronger for 100 rupees and if you select "Yes" and you have at least 100 rupees, a text box will come up asking you to press start and if during that text box, you press a c-button that has gold dust on it, they will take your gold dust and razor sword if you come back and talk to them on Day 3, they will give you a guilded sword with an attack strength of 3. You can also sell them gold dust for 40 rupees. The guilded sword will never turn back into a lower sword upgrade. All 3 swords, just like deku sticks and the great fairy's sword, do double the damage with a jump attack. In the Japanese version, there's a glitch called Power Crouch Stabbing where a crouch stab does the same amount of damage as the previous attack of any sword like object.
You start the game with the hero's shield. If you get sucked up by a like like in human form with the hero's shield, it will take your shield and you can get it back if you defeat the like like without first leaving the area. You can also buy a hero's shield in West Clock Town for 80 rupees or the Zora Shop for 90 rupees if your shield is gone. The treasure chest at the end of the Ikana well has a mirror shield in it. Once you open it, it overwrites the hero's shield if you have one. You can crouch in a spotlight from lit by a hole in the ceiling to reflect that light with the mirror shield and if you direct the reflected light towards a sun block, that block will disappear. The mirror shield can never be lost once you have it.
You start the game with no bomb bag. Without a bomb bag, no bomb drops will appear and you can't buy any bombs or bombchus. You can't play in the honey and darlings's shop on the first or second day without a bomb bag either. All treasure chests that normally give you bombchus give you a blue rupee if you don't have a bomb bag. The bomb shop has a regular bomb bag that you can buy for 50 rupees if you don't have a bomb bag. If you make Sakon drop the bomb bag, the bomb shop will be selling the big bomb bag instead of a regular bomb bag for 90 rupees immediately after the cutscene of having stopped him. If you don't defeat him, the bomb shop will make no change to what they sell and the big bomb bag will become available to buy at the curiosity shop for 100 rupees on the night of the 3rd day. It opens at 10 pm but you can also torch clip then hover into the curiosity shop to get in earlier on that night. You can buy the big bomb bag if you have the regular bomb bag or if you have no bomb bag. The only way to get the biggest bomb bag is to talk to the deku scrub that started off in Goron Village in goron form before he moves to Southern Swamp or any form after and give him your big bomb bag and 200 rupees. You can't buy a bomb bag you already have or one that is less good than the one you have. The regular bomb bag can hold up to 20 bombs and 20 bombchus; the big bomb bag can hold up to 30 bombs and 30 bombchus, and the biggest bomb bag can hold up to 40 bombs and 40 bombchus. Every time you get a bomb bag, it comes with the maximum number of bombs it can hold. On the other hand, no bombchus come with any bomb bag upgrades and when ever you get one, you keep the number of bombchus you already had.
You get the smallest quiver when you get the bow. The smallest quiver holds 30 arrows; the medium one holds 40 arrows, and the biggest one holds 50 arrows. You get one upgrade when you score at least 40 points at the octorock shooting gallery and the other upgrade when you get perfect at the swarm shooting gallery. You can get the two upgrades in either order. You can't play in a shooting gallery unless you have a bow. Every time you get a quiver upgrade, it comes with the maximum number of arrows it can hold.
You start the game an empty child's wallet that can hold a maximum of 99. The next upgrade is the adult's wallet which can hold a maximum of 200 rupees and the one after that is the giant's wallet which can hold a maximum of 500 rupees. One upgrade is gotten by making there be at least 200 rupees in the bank for the first time and the other wallet upgrade is gotten by beating the Ocean Spider House then talking to the guy at its entrance on the first day. He will give you a purple rupee if you talk to him after beating it on the second day and a red rupee if you do it on the final day. Also, if you talk to him after beating it on the first day and you already got the wallet upgrade from him, you get a silver rupee. You can get the two upgrades in either order. You don't get any rupees when you get a wallet upgrade.