A few questions about homepage redirects:

I want my homepage to always be http://www.mydomain.com/

I've had the following code in my htaccess for awhile in order to make sure that http://www.mydomain.com/index.html is redirected to http://www.mydomain.com/ (at least I think that's what it's for).

RewriteEngine on
RewriteCond %{THE_REQUEST} ^[A-Z]{3,9}\ /index\.html\ HTTP/
RewriteRule ^index\.html$ http://www.mydomain.com/ [R=301,L]

Do I also need to add separate code such as that below to redirect http://mydomain.com/ to http://www.mydomain.com/? Or does the above code accomplish both? (Because both redirects seem to be already working, I'm just not sure why it's already redirecting for http://mydomain.com/)

RewriteEngine on
RewriteCond % ^mydomain.com [NC]
RewriteRule ^(.*)$ http://www.mydomain.com/$1 [L,R=301]

Also, is it necessary to set the preferred domain in google webmaster tools to www.mydomain.com if I am using these 301 redirects?