When does the crate counter reset?

In PUBG, every time you buy a crate, a counter increases and the next crate costs you more.

I've seen this going back to crate #1, but can't figure out when that reset happens. Is it weekly, monthly, decided by player unknown (resetting on updates)?

Also, does going for a higher box give you a better reward?

The crate reset time is Monday 0:00 UTC (thus it is weekly). A helpful timer can be found here.

As for the rarity, the price does not seem to matter. Reading this steam post seems to indicate this. From personal experience a well, it seems this way. They also mention the crate timer resetting on Monday as well.

All the boxes are 100% the same, price does not matter - 700, 1400, 2800, ... 7000. It all drops the same. Price resets every monday.

Note that depending on your time zone, it may be Sunday when the crate cost resets, but it will reset at the same time no matter what for everyone.