I am new to all of this also.  From what I understand, you would want to start with the Quick Phonemic Awareness Assessment (from the PRESS Assessment Manual) for kindergarten.  This information gives you a starting point (PA-1, etc).  Again, from what I understand, this works in a progression, so once a student has a particular skill down, you would check the next area of the Quick PA Assessment.  Personally, for kindergarten, I have given both the Quick PA Assessment and the Decoding Inventory.  We work on PA and phonics at the same time, so I wanted to make sure I also hit letter/sound correspondence for those students who come in not knowing many letters or sounds.

For grades 1-3, I started with the Decoding Inventory.  This also works in a progression, so once you hit a frustration point, you can discontinue and that is your starting point for intervention.  I did have a few first grade students who were very low on their letter/sound correspondence, so I went back and did the Quick PA Assessment.

I like your stopping point question.  My thoughts...you will attempt to get the student to the highest mastery for each grade level.  CVC words would be appropriate for kindergarten, but we don't expect a kindergartener to be fluent in CCVC words, digraphs, etc, so it isn't necessary to "intervene" on these skills.  (Unless you have an exceptional group and those children need the intervention to keep up with the other students in the class.)  

We eventually developed flowcharts for K-2 which show how far we advance in PRESS based on grade level and classroom introduction of skill at what time of year.

Would you be willing to share the flowcharts you created?