How can I *rightly* track my users... usage

Hi!

I’d like to track my users a bit more than what basic Google Analytics reports can provide me.
How can I do that in a smart way? I’d like to see if they come back, if they use the app.
What do you think would make sense to track?

Basic feature of the website is to look for a food ingredient, and that tells you specific data about it.
So key info is the queries made, I’m already loging them but as it’s a simple Input search item, I’m only loging when they hit the “OK” button, and it’s actually not necessary to tap that button, so I’m “losing” all those that skip it (results load in the repeating group without it!).

Some users have Premium rights and create accounts, others are just browsing through the website.
So knowing when they log in would make sense, but as I have users coming back everyday, most actually don’t need to log in again, they’re already in.

Thanks for your input!