Generally speaking, Tradition or Liberty doesn't matter much for Austria. That just depends on how the map shapes out to be. Aggressive neighbors/lots of room to expand? Liberty. Otherwise, Tradition.
As for buying CS, I only buy those that are either adjacent to my empire (And therefore easy to defend) or have strategics that I need. I rarely end up buying more than 3 CS's over the course of a game (And I play with 22 CS). Also, I prefer to buy Religious and Militaristic CS first, as the benefits of Maritime, Cultural and Mercantile CS's are too big to ignore, but if you have the happiness, Mercantile is also a good target.
Another way to play Austria however focusses on supplying Vienna with food trade routes (So a coastal Vienna would be preferred here), and get all the Great Person Boosting buildings there, along with the Coffee House, giving you another 25% bonus. Buy up other coastal CS to give you even more food trade routes, get Tradition (Hanging Gardens are a must if you have no normal garden possibility) and try to grab the Collossus. This strategy isn't as strong on higher difficulty levels though.