New Frontier provided a self-contained corner of the Alpha Quadrant written entirely by Peter David, carrying the consequences from one story to the next. For over twenty years, the adventures of Captain Calhoun have entertained fans of Star Trek and created a bedrock to let publishers know fans were willing to follow original characters into the void. Thanks to the existence of Discovery, Star Trek is no longer in need of the Expanded Universe to continue its legacy [though I hope it continues as its own thing for as long as possible] but I still love these classic books written by Peter David. So what do I have to say about this series, now that I've talked it up for so long? It is very-very silly. Awesome but silly.
No, seriously, that's what you should understand before you pick up this volume and read a word of it. Peter David is a comic book writer, one of my favorite if not my favorite, and I mean that in both tenses of the word. The adventures of Captain Calhoun and his wacky crew trump the Original Series in terms of ridiculousness, are often prone to comedy skits, and include a race of Ewok-shaped evil wizards. If the idea of a planet-sized egg for a being not-too-dissimilar to the Phoenix from the X-men comics offends you, this may not be the series for you.
The strange thing is, New Frontier is still capable of generating drama and pathos despite its occasional verges into utter insanity. I care about the characters of the U.S.S. Excalibur more than I care about a lot of fictional characters. The death of billions during the Star Trek Destiny series affected me less than than the loss of some crew members here. This is definitely a book series where your mileage may vary but I recommend checking them out just in case. I freely admit it was a strong influence on my writing and helped make me the die hard satirical nerd I am in books like The Rules of Supervillainy and Lucifer's Star.
Now that I've discussed the series as a whole to death, I'll mention the omnibus itself. It's not actually an omnibus but the original novel that the publishers broke into four novellas for reasons of, "we believe it'll sell better this way." The premise is brilliance in itself and I've replicated it a dozen times for my tabletop Star Trek games. A big Romulan Empire-sized territory called the Thallonian Empire has collapsed, leaving dozens of star systems anarchic and without leadership. The Federation, fearing a humanitarian crisis on an epic scale, sends a lone starship into the chaos to patch things up. It is captained by the second most renegade/rules-ignoring Captain in Starfleet history (the most being Chris Pine's Captain Kirk).
Captain Mackenzie Calhoun is a former planetary warlord who joined Starfleet after liberating his planet from oppressive alien rule. He's also spent the past six years on undercover assignments for Admiral Nechayev, doing the sorts of things Section 31 would do if it had been invented yet out-of-universe. His crew is a similar collection of misfits including straight woman Shelby from "The Best of Both Worlds", Robin Lefler (Wesley's girlfriend played by Ashley Judd), a hermaphrodite alien engineer, one-off TNG character Selar, an exiled alien dictator, and the cast from Peter David's Starfleet Academy books. It's not the sort of cast which immediately excites you but the way they interact is delightful. Assuming, you know, you throw out all sense that Starfleet has any discipline whatsoever.
This is a book filled with action, adventure, comedy, and oddball office quirks that somehow don't detract from the story. Peter David did something very much as we'd think of as "Whedon-esque" humor well before Whedon had hit it big. This is because he combines his comic book writing skills with a deep love of Star Trek's lore to create something bizarre. This is clearly the oddest ship in the Federation and that's not a bad place to be.
The first four books aren't perfect. I'm not too fond of the way that Shelby conducts herself around Calhoun, I think Burgoyne (the hermaphrodite engineer) treats Selar in a manner dangerously close to sexual harassment, and the best moments for our captain are usually when his brother is humiliating him. Despite this, the humor and sense of adventure is nearly beyond compare in the EU. Check them out, I suspect you'll find them well worth it.