If I go to quick edit for a page I can choose from two templates .. front page and default template .. I chose front page because I am building a website, not just a blog. In fact it will, if all goes to plan, have about 10 static pages and one blog page.
The problem is that you're selecting your Site Front Page in the wrong place. :)
Go to Dashboard -> Settings -> Reading, and change Front page displays from "Your latest posts" to "A static page".
Then, immediately beneath that option, use the dropdowns to select the static Pages to use for your site front page and blog posts index.
Once you've done that, WordPress will automatically apply the Front Page template to the page you've set as the front page.
On my static pages I want to use a two column layout (left sidebar and main entry on right) along with a header and footer of course. I went into appearance|oenology|layout and set every option to two columns.
Perfect so far...
I went to widgets and created a text box in the left sidebar. It DOES show up but only in the front page template, along with many other widgets. In the default template it is not there.
Try setting the front page correctly, as above, and see if the problem persists.
It would seem from a neophyte's point of view that there should be widget placement options for each page template but there doesn't appear to be.
Such functionality requires the use of a Plugin. I love Widget Logic for just this purpose, but there are other Plugins that might be more new-user friendly.
I guess because of the consequent confusion/interplay between layout options, page templates, and widget placement I would like to make some pages that always work the same way, thus maybe making a series of page templates that have widgets in place, like the front page template seems to do. Really I don't need to do this IF I can figure out how all these consistently interact.
Sorry if I'm making this confusing ..
No problem at all! I think the main problem is the one detailed above. Let's fix that, and then see what issues you still have.