Once the gallery is published on the web, I will need to be able to copy and paste URL's that will function as links to specific images.
Setting enableDirectLinks="TRUE" in your gallery's XML file would allow you to link directly to individual images within a Juicebox gallery by using URLs such as: http://www.example.com/gallery#2
Please note that enableDirectLinks is a Juicebox-Pro option (which is not available in Juicebox-Lite).
Also, I want the potential to exist for search engines to find specific images based on words in its description or title.
This is not possible with Juicebox-Pro out-of-the-box but may be possible by implementing this technique (though it may be rather complex to achieve). You would first need to implement a new direct linking technique (as Juicebox natively uses # rather than #!) and you would also need to provide HTML snapshots. All of this can perhaps be achieved for a web site containing a Juicebox gallery but it cannot all be integrated within Juicebox itself.
I know that I am going to want something that is HTML5 based, not Flash. Also, considering my lack of experience designing a website, Showkase sounds like it might be the right tool for me.
Showkase would certainly allow you to create a portfolio website with no coding knowledge (please see the Showkase Site Demos here), and Juicebox is, indeed, an HTML5 (non-Flash) image viewer but using Juicebox in conjunction with Showkase would not solve your SEO wishes.