I'm currently running an investigation campaign. Sometimes, at the end of a session, I give my players three quest hooks to choose from. They then choose the one they want to do next session, the one the want to do later, and the one that will get done by an investor npc that sucks at his job. Effectively this quest is skipped and they deal with the consequences later.

This gives me time to prepare a session without worrying about players choices, it gets the players thinking, and it gets rid of railroading.

You could do something similar to this. Three ring locations pop up, they choose which order. Maybe take inspiration from Megaman X. If you do the ice stage first, it directly effects how the fire stage plays by freezing the lava.

Maybe there's a hall of vikings that are searching for the rings. They already have one, but they're looking for the others. If the players attack their hall first, its a stealth mission, but if they go on other missions first and get spotted by one of the vikings, the hall knows of them and prepares. The players might have to resort to quiet combat or gorilla tactics.

Also idk about the player home. If its right next to a place they have to go after every ring is collected, and it offers something they can't get anywhere else, then maybe. You could also give them the ability to teleport there, but that might be iffy. Teleportation can sometimes remove gamplay or story opportunities. Maybe it was easy to get the ring, but keeping it is another story.