The above redirect structure you've proposed would work great. You're ensuring only one homepage version exists, making it the canonical, and all variations (which may also have previous links going to them and SEO value) are being redirected to pass on to the canonical version.
You can use your .htaccess file to force http to https by adding the following code:
RewriteEngine On
RewriteCond %{HTTPS} !=on
RewriteRule ^.*$ https://%{SERVER_NAME}%{REQUEST_URI} [R,L]
The first line turns on redirection capabilities. The second line checks to make sure the connection is not already https. The third rule will redirect users from their original location, to the same location but using HTTPS.
And also, in case you want to know how to make sure that the www. version of your site redirects to the non-www version, the code would be:
RewriteCond %{HTTPS} on
RewriteCond %{HTTP_HOST} ^www.(.)$ [NC]
RewriteRule ^(.)$ https://%1/$1 [R=301,L]
Hope this helps