Two of the most popular (and FREE) screencasting tools are Screencastify and Loom. Both are great, so whichever one you choose, you can't lose!
Screencastify does seamlessly interface with your Google Apps (it is an extension for your Google browser and Gsuite account).
But, Loom gives teachers a "pro" level account with no time limit. More info on that can be found here:
https://support.loom.com/hc/en-us/articles/360006579637-Loom-Pro-Free-for-Students-and-Teachers
At the bottom of this page, check out a great video comparing the two different tools (spoiler alert: the experts determined that the comparison came out to pretty much a tie).