Doing the Two Step
It turns out the key to getting things to work is to leave the username and password areas blank for the Outgoing Mail Server area. If that is done, then when I hit save at least the incoming mail portion would work, although as I said it now wasn't using SSL. This struck me as not such a good idea since the iPad is using Wi-Fi to send everything.
Once I had tested incoming mail in the mail app, I went back to the preferences to work on getting SSL to work and getting the outgoing mail to work. I started with the button for the GoDaddy account for my company as shown at the left.
First I wanted to change the incoming mail server options so I scrolled down to the "Advanced" button,(see the green arrow in the image at the left).
In this panel I turned on SSL and changed the incoming server port to 995. (If you don't use GoDaddy your port number may vary and you'll need to search around your email provider's site to find the proper port number to use for SSL connections).
Now it was time to update the outgoing mail server settings. I went back to my account page where I had selected the Advanced button. This time I selected the SMTP button under Outgoing Mail Server (see the blue dashed arrow in the image up above).On the resulting screen I selected the Primary Server button as shown in the image to the left.
Finally, I turned the Server ON, turned on SSL and set the Server Port to 465. Upon returning to the main account screen (clicking Done or Save where appropriate) I was rewarded with a series of checkmarks on each section. I then booted the email application and was able to both send and receive mail.Also, one final iPad tip. You can take screenshots of your iPad by holding down the rectangular wake/sleep button on the top right edge while clicking the round Home button in the bottom center of the screen. If you have the volume turned on you'll hear a camera click and the screen will flash. The image will end up in the photo application and you can upload it to your computer when you sync. Alternately you could email the photo to yourself, now that you have email working.
Since this post is getting a lot of traffic I thought it was worth bringing attention to a fix mentioned in the comments below that worked for at least two users:
When you are configuring your outgoing server, put in your username and password where it says optional.