Hi Richard,
It depends in part on where you see your work focussing. I wasn't at the conference to get all the scoop on Tessitura's plans for the next phase of business intelligence, but for the forseeable future reporting will still be based on SQL, and most customizations will still require it, especially if those customizations involve storing custom data.
Then REST API is, of course, where Tessitura hopes that customization will largely go in the future, but frankly that's still a way off, at least from my own experiences working with it. The API itself is actually pretty agnostic about what it requires to work with it. It accepts and returns either XML or JSON (although it's important to note that only passing familiarity with those protocols is required), and it can be consumed and driven by essentially any programming language or framework capable for making HTTP requests; e.g. PHP+cURL http://php.net/manual/en/book.curl.php. I mention that cURL because I'm in the middle of a data sharing project where I have created and exposed tables through the "dataservice" part of the Tessitura REST API, and our partner is consuming it with cURL.
C# and .NET, however, have the advantage of being what Tessitura themselves use, and thus there is a set of client libraries with convenience functions available from them.
But you don't have to start there to get your feet wet. With a browser on a machine capable of conneting to your API server you can manually enter in REST commands and start getting a handle on what is possible immediately.