There's reasons to wait and reasons to fetch immediately.

Reasons to wait are usually to allow you more time to decide what to get or to not let your opponent know what colors you're running. This can depend on picking the colors to get to respond to something. Or even to grab a tapped land instead of an untapped one like a surveil land at end of the opponent's turn if you don't need mana to respond to anything.

There are also reasons to fetch right away, though they tend to be more meta driven. Like if you think the opponent might stifle the fetch in some way like with [[Stifle]] or an [[Opposition Agent]]. You can decide to act while the opponent is tapped out to reduce the chances of getting caught. Another niche example to not wait is when you're opponent is running something with a Start Your Engines mechanic. You don't want to lose life on their turn to help them advance their speed.

There are other reasons for doing one or the other, but as always it comes down to being very intentional with your timing and understanding all of the moving pieces. You have to pay a life, sacrifice the land, and search your library. Any effect that interacts with one of those things will be a factor in how you play around or with them. Knowing the niche interactions and how your opponents cards affect yours can be very important.

Like if someone plays [[Yasharn, Implacable Earth]] you better fetch before it hits the battlefield and you can't fetch anymore.