I completely agree with you about the lack of attention paid to Maurice (or even any of the early Byzantine emperors apart from Justinian...)! I can't think of any good introductory text for Philippicus or Maurice unfortunately, since even academic historians haven't written a lot of stuff on them. The main problem is the lack of sources and the way we've interpreted them. The main source for the career of Philippicus is Theophylact Simocatta, who wrote a history of Maurice's reign during the reign of Heraclius. The basic narrative isn't a problem, but Theophylact was also regurgating Heraclian propaganda by depicting Maurice as this wonderful emperor who was brought down by a tyrannical usurper. Based on contemporary sources, it is clear that Maurice was terribly unpopular despite his massive victories over Persia and the Avars, so I think Theophylact's depictions of Maurice and Philippicus are simply too positive to be 100% reliable. Plus, Theophylact is a pain to read since he used really fancy Greek and wrote rather flamboyantly. Still, if you think you can handle it, Mary and Michael Whitby did a translation of the text in 1986 and they also wrote a book analysing it, The Emperor Maurice and His Historian (1988), which is still the standard text used for this topic (in English anyway).

Philippicus' later career is also discussed in Kaegi's Heraclius (2003), but only briefly. I don't think there are any other books that cover this in a relatively straightforward way I'm afraid - I actually think Kaegi's analysis of Heraclius isn't great, but it is at least fairly accessible for a novice. To get a sense of what modern academics think, check out Schlosser's The Reign of the Emperor Maurikios (1994) and Olster's The Politics of Usurpation in the Seventh Century (1993). Both books were written for academics, but they do a really good job of summarising what modern scholars think, especially Schlosser. Olster is a bit more interesting, since his thesis basically rehabilitated Phocas from Heraclian propaganda and provided an excellent reconstruction of Maurice and Phocas' reigns. His influence is enormous and I don't think any historians these days would still see Phocas as a brutal tyrant or Heraclius as the saviour of Byzantium; the former was actually fairly competent, whilst the latter's revolt was key to the collapse of the Byzantine war-effort against the Persians, not Phocas' policies.

Here's a list of the sources mentioning Maurice and have modern translation, some of which you might be able to find in a library/second-hand bookshop :) Not surprisingly, the contemporary sources are all pretty critical of the emperor, except the ones who were commissioned by Maurice of course!

• Austrasian Letters: Frankish queen wanted Maurice to give back her grandson. Maurice said no.
• Gregory the Great: The pope got increasingly frustrated with emperor's policies.
• John of Ephesus: Maurice treated miaphysite Christians and his Arab auxiliaries horribly.
• Life of Theodore of Sykeon (early seventh century): Maurice was just executed? He totally deserved it.
• Pseudo-Sebeos (660s): Maurice treated Armenians horribly.
• Miracles of St Demetrius (mid-seventh century): Maurice wanted a relic from the saint, saint miraculously told him no.
• John of Nikiu (late seventh century): Maurice treated Egyptians horribly.

And here are the sources commissioned by or related to Maurice:

• Menander Protector: Actually a history of Tiberius II's reign, but in the prologue mentioned what a wonderful guy Maurice was.
• Evagrius Scholasticus: Again not really about the reign of Maurice, but was rewarded handsomely for his ecclesiastical history written during Maurice's reign.
• Strategikon: A military handbook for fighting against barbarians, provides a good insight into how his armies worked.