Hi Bonnie,
To schedule a process chain in BW, try the below option,
If you double click the start (first unique process in a process chain) variant you can able to see the scheduler option.in that scheduler direct scheduling tab, instead of immediate scheduling set the near saturday date and time in the scheduler and also set it to schefule on weekly basis.After this settings save , activate and schedule your process chain. This will ensure to run your process chain on weekly basis.
To run it on a first saturday of every month, create a custom program which has to give you the date details of first saturday of a month.
Create an event variant and pass the date details to this variant.In this way it'll work.
-Arun.M.D