Hey look, a familiar face! Great to see you back on the forums. With RC3 coming out over a year ago, I'm a little rusty on the changes but I'll do my best to address the steps you'll face. If you had to make any serious hacks at that time, let me know and there may be equivalents now, or even functions that help.
Static Pages: In version RC3 (for those who weren't w/ us a year ago, we had a set of release clients before ever putting out 0.9) you could create new pages on your site by including separate files in your theme. If you created a dave.php file in your theme, it would automatically create a new URL and static page (youromekasite.com/dave/).. that 'feature?' is gone. We've replaced it w/ the SimplePages plugin that allows you to create and static pages and their routes via Omeka's back-end. It should be easy to edit and maintain these pages.
Contribution Plugin: I'm pretty sure the updated version will work the same as your version -- you'll obviously need to style the CSS similar to your site.
Otherwise, I think you'll be fine. I'd approach updating the theme by just running with it, and referencing our up-to-date themes for how functions on the homepage (such as recently added items), as well as the items show and browse pages work. You should be able to copy the basic logic from the updated themes to suit your needs.
Good luck, and let us know if you run into any problems.