How to exclusively use HTTPS from the start in Wordpress

Morning everyone.

I have a project that is to be completely https right from the start.

I know that some will think that is a crazy thing to do because of the extra work encrypting data but, since over 90% of the visits (and activity in the site) will need to be over SSL, it makes sense to use HTTPS exclusively than just drop in https links as and when required.

I created a test install of WP and then set the site URL in Settings to https (Site address (URL)) which forced all the pages to be loaded via https but it doesn't force images (media library) to get a https URL when adding new media.

If I change the WordPress address (URL) to https I can't log in any more, but I suspect this is the URL change that would force all new media (images added to the library) to be given a https URL.

I notice that there are a few ways of changing content on the fly with functions or javascript but, if possible, I'd like to have all this done without adding extra plugins etc.,

Has anyone done this? Please can you tell me how to build https in from the ground up so that all pages, posts, images (etc) are given an https URL?

Thanks.

Martin