Debian - Apache - User - Which chown?

I think the best way to do this is to do use your first option:

chown -R www-data:www-data mysite/ 

But then add your user to the www-data group

usermod -a -G www-data user

and then give the group control over the files

chmod 770 -R /var/www/mysite

Chmod 770 basically means both the user who owns the file (in this case www-data) can do read-write-execute and all users in the group assigned to the file (in this case www-data as well) can do read-write-execute.