CPO,

Prior to recieving your private, you can only log PIC if you're the only person in the aircraft (solo). After that, you can log both PIC and dual recieved if you're rated for the category and class of aircraft you're in. An example of this would be your instrument rating or your commercial single. While legal, some airlines don't count this as PIC for their hiring minimums.

Something I would suggest for you to put in your back pocket for later which will save you money (contrary to LAFF's belief CFI's aren't all out there to steal your money and log that extra 0.1) Take a private-multi ride if you intend on being a CFI. You'll need 15 hours multi PIC to get your MEI. If you have the pvt-mel you'll be able to log all that time working on the commercial as PIC. In the long run this could save you a ton of money by avoiding 15 hours at $200-300 an hour down the line.