Is this how you hash a password correctly? PHP+MYSQL

Hi!

I'm kind of new to the whole php, mysql safety thinking. I'm currently building a site for my dad, which needs an admin panel. I'm trying to make it somewhat secure.

First thing I did was echoing out password_hash('therealpassword', PASSWORD_DEFAULT), then copy+paste the result into the database where the pass goes (also making sure max characters are set to 255, since I'm using PASSWORD_DEFAULT).

I also stored the hashed password into $stored_password in the php login file for comparison with userinput stored in $password.

Then I verify the userinput with the password in the database:

if(password_verify("$password", $stored_password){
//sql, session, header etc.
}

I also used mysqli_real_escape_string on the user input after storing them in variables and before using them in the sql-statements.

Am I on the right track here?

Thanks.