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.