After reading through this post and many others, I achieved what I wanted. Here's a summary so it's all in one place:
What I wanted:
"Home" in navigation bar, footer and breadcrumbs to point to https://www.mysite.com, not to https://www.mysite.com/store
Compromise:
I changed it for navigation bar and footer, but you can't change it in breadcrumbs without editing core files. So instead, I removed the 'home' link from breadcrumbs.
How to do it:
(Assumes you are familiar with the overrides system!)
Make copies of these files for editing:
includes/templates/template_default/common/tpl_header
includes/templates/template_default/common/tpl_footer
(or if you've already edited them get them from your custom overrides folder)
In both files, change this:
. HTTP_SERVER . DIR_WS_CATALOG .
to this:
. HTTP_SERVER .
(pay attention to the dots!)
There is only one instance in tpl_footer; there are two in tpl_header.
Upload the edited files to your custom overrides folder.
That takes care of navigation bar and footer.
Now, to remove 'home' from the breadcrumbs:
Go here:
http://www.zen-cart.com/forum/showthread.php?t=35299
and follow the instruction in Post #8.
NOTE that when he says upload the file to the "overrides" folder, he means that literally. There is already a folder there named "overrides". You are to put the edited file "init_add_crumbs.php" into the directory "includes/init_includes/overrides".