Is P'suqe d'Zimrah obligatory?
It is true that Hazal do not state that P'suqe d'Zimrah is obligatory. This is implied clearly by the Talmud's choice of words (Bavli Shabbath 118b) and is confirmed by Rambam's precise formulation: "The Sages praised highly he who recites certain selections from Psalms daily..." (Hilkhoth T'phillah 7:12).
Such a recommendation of the Sages, while not obligatory, carries a lot of weight. Thus, under normal circumstances one should indeed say P'suqe d'Zimrah.
If one is running late for work etc., or arrives late to a minyan - it is better to say the essential prayers (Q'riyath Sh'ma and 18 B'rakhoth) without rushing, or to say these with the minyan, rather than insist upon reciting P'suqe d'Zimrah.
If one has already said Sh'ma and Tephillah, can/should one say P'suqe d'Zimrah?
P'suqe d'Zimrah is a preparation for T'phillah. If one has already read Sh'ma and prayed the 18 B'rakhoth, P'suqe d'Zimrah is no longer required and one may not say the B'rakhoth (Barukh SheAmar & Yishtabah) (see Arokh HaShulhan OH 52:5).