Hi Kashish!
I highly suggest you use Jest for both client and server side tests. It's an fantastic testing framework. And with the relatively new projects feature that allows you to run both client and server tests at the same time, I think you'll be really happy with it. You should also have E2E tests that run in a real browser. I recommend Cypress.io for those.
I actually have a course on FrontendMasters.com right now about testing that uses these tools. I'm going to be creating two new testing courses that are similar but more in depth and I'll be using the same repo except entirely rewritten and simplified. You can find the repo (currently on the v2 branch) here: git.io/testing-workshop. It's still a work in progress, but hopefully that'll be helpful.
Good luck!