Minimize database queries to user tables?

You made a lot of statements here, so let’s go through them bit by bit.

while keeping database queries low

The amount of queries isn’t directly an issue, time that they take is. Single really slow query can take more time than hundreds of very fast ones.

before the website loads (or the first time a website loads)

Since WP is PHP application every load includes full cycle and is not persistent. There is no “first time” because it starts from nothing every load. The only persistent parts are those that are saved into database or otherwise.

Would the information save on visit (cached on browser), or would it be necessary to use the transient api?

Browser caching, while important, does little to help you improve performance of site itself. Transients are precisely kind of persistent storage appropriate for such use cases.

However, as usual with performance tasks, it is hard to recommend anything without profiling the slow operation. It is exceedingly easy to make faulty assumptions about reasons of slow performance and waste time trying to address them.

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