How should checklist be stored in the database from atomic point of view?

I recently come across saving a checklist in a database and I was a bit lost. Then I decided to save it in one column, as comma separated values and it worked great. But now I am implementing the same in a different project and want to know what is best way to implement it from database point of view. Take this as an example

This is an example of one-to-many relationship. A single user may like different cars. The best approach from database point of view in normalized form is

id check_id check_name

The problem is this will require separate SQL queries and saving and change options would become more complex (would need deleted addition rather than simple update). Note that from database best practice point of view, we want to save only atomic data, so saving comma separated values in on column is not recommended.

My question is,

1. What is the best practice to implement checkboxes in database?
2. Is comma separated values better or a separate table for options? Does one provide more flexiblity down the road (eg. we want to add more companaies in option)
3. Is there any performance difference? What the normalized design show any enhancement, such as in search etc, that the other one does not have?