The primary consideration in choosing a partitioning key with DPF is to avoid cross-partition joins (along with even distribution of data among the partitions).
If you have only one fact table in your Star Schema, then just about any reasonable partitioning key can be used. But you need to replicate all the small dimension tables on each partition (so a copy of each dimension table is on each partition) to avoid cross-partition joins with the fact table.
If you have multiple fact tables that may be joined together (I am not talking about 2 unrelated fact tables that will never be joined), then it is a bit more complicated and if possible you should choose a partitioning key that is the same for both tables (so long as it produces an even distribution of data across the partitions). Again, the purpose of doing that is to eliminate cross partition joins.
If you follow the above guidelines, you will be 90% of the way home toward high performance parallel query processing.