Great idea. You have much to offer in allowing a site to graduate. In my personal loose order of priority, with an estimated amount of time you have to invest in parentheses
definitely first removing the beta label and giving a huge sense of security to the community and the rest of the internet
(2 mins, a meta post saying "Congratulations! You made it!")bug fixes that are particular to a community (internationalization, etc.)
(several hours of developer time, but possibly less if you allow the community to help)moderator elections (10 mins developer time)
Community Ads
(10 mins developer time)...
definitely last a shiny new design
(possibly weeks of developer time)
Work in order of the list, just ensure that you scale your hiring to get to the last step eventually. (I still think a nice shiny design is an important last step, not at last for presentability and for the Stack Exchange image.)
In fact, some unofficial comments which give a "tentative list for graduation" are already floating around the network, but they don't have any of the good reassuring effects. Why not make them official? (It's not like people are going to say, "oh, we're graduating? I guess I can take some time off now...". Everyone's excited to be here already.)
Maybe keep an updated public list of individual progress of recognized-graduated sites. We all know you have many priorities and making a site design shouldn't be your first priority and we won't be angry if you run a bit behind schedule (because you're low on staff or because you just haven't found the right guy/girl for the job).
