How to increase the number of "Recent Entries" showing in the left sidebar list.
Step 1) If you open up left_bar.php in the neoclassical theme and find this:
I believe you can change the maximum number of posts that the theme will show using the default left sidebar. For example, if you change it to: query_posts('showposts=25'); then you should be able to show 25 posts...
Step 2) open /wp-includes/default-widgets.php and at line 542 and 543 you will find this:
else if ( $number > 15 )
$number = 15;
Change the "15"s to "25" and save your changes.
Note: This is a core file. Make a solid backup of your files first, if you should decide to try this.
If you are using the "Recent Posts" widget to display these, this should now allow you to now increase the maximum value of "15" (inside the widget) to any value up to and including "25". In fact I think you will have to change it, or you may still be limited to whatever value is set in the widget. I think that should work, but you might want to experiment with it a bit. Back up your files first, just in case.
I'm hoping that someone will suggest for you an easier method of over-riding the 15 post setting located in default-widgets.php. Perhaps something in the form of a simple filter to add to your theme files. I'm afraid I'm just not sharp enough to construct one that I believe would work properly. Don't forget, if you decide to edit a wordpress core file, you could loose the changes on the next upgrade, so be prepared for that.
I was thinking I could also add an "Archive" widget below the "Recent Entries"
You should be able to add the archives widget right under the recent posts widget in the sidebar. I think the left sidebar is referred to as "sidebar 1" in your dashboard. I don't think that should give you any trouble. As far as customizing the output, that's a little out of my depth I'm afraid.
Good luck to you, and don't do anything you can't undo!
 just an after thought. It might be worth browsing through the plugins. Perhaps someone has already come up with something to make this really easy.