Is having a database handle open through the whole runtime good practice?

I did some research and may have missed better keywords for what I want to find out:

• Is it good practice to have something like a init_db() function that gives me a handler of the database at startup of a program and then close it when I exit the application.

Maybe to put more context: I'm trying to build a server executable in C, that should (in the best case) run non-stop / until updated, accessing a SQLite db.

• Also at what scale should I change from SQLite to MySQL. Maybe transactions per minute or size of db. Is there any chart for this?

Thanks!