>I am attempting to update a new computer OS from Windows 8 to Windows 8.1 (tell me if I shouldn't do it).
>But when I click on the Microsoft Store I see a bunch of stuff that MS is trying to sell but no tile for Windows 8.1 upgrade? And no search button.
>What am I missing?

I would say you definitely should.

The installation over 8 will ask you if you wish to wipe it out completely and offering you the chance to keep your user profile settings. I did that in 5 minutes and it worked on the first try. The user settings have been preserved. More than that, if you had a VHD, that will be preserved as well.