At last, my time has come. Annoyingly long essay under the cut because I've read 200 of these things and none of my IRLs can match my freak so I have 15+ years and a twelve-sheet spreadsheet of opinions stored up.
First of all, I will start by saying what I say when someone asks me which Star Trek show they should watch first: It depends on what you want out of the experience. The person who loves DS9 is not always going to adore TNG, and the person who adores SNW might bounce hard off TOS. The same is true with the novels (though, if you are reading Star Trek novels, I assume you are a hardcore fan and have more of a tolerance for poking around in stuff you might not enjoy in order to find the stuff you do enjoy).
That being said, it's helpful to know what you're looking for before you dive head first into 60 years of tie-in literature spanning hundreds and hundreds of books. Personally, I like my sci-fi to have minimal space battles, great character moments, and imaginatively alien worldbuilding, so my recommendations are going to skew toward novels that contain those. If you're more into the hard sci-fi and/or space battles and/or alien-of-the-week plots, take my recommendations with a grain of salt and DuckDuckGo some "best of" lists to supplement them (here are two to get you started).
Generally speaking, I would recommend entering the tie-in fiction universe by way of your favorite series (provided it has books). TOS, TNG, DS9, and VOY all have numbered and unnumbered novels, while ENT, DISCO, PIC, and SNW are all unnumbered (ENT is an edge case and shouldn't really be lumped in with those others, but I'll get to that eventually). There are also truly staggering amounts of OC/backstory/spin-off/tie-in fiction exclusive material housed in series like New Frontier, S.C.E, and Titan, so if you love the Star Trek universe but aren't necessarily attached to a specific set of characters, these are great offshoots to explore.
The numbered novels usually do not need to be read in order unless they're part of a mini- or cross-series arc; they tend to be stand-alone and don't do anything to disrupt canon (a lot of the TNG, DS9, and VOY novels were published during the shows' runs so they literally couldn't disrupt canon). There are some really good books in these lines and some really bad books also and a lot of three stars fine books in between, so if you strike gold on your first try don't get discouraged if the next one you read is garbage. It happens. There's another amazing book just around the corner, I promise.
If I were to over-simplify it, I'd say that the quality of the numbered novels falls off the further they go on (early TOS numbered novels have some astonishingly creative worldbuilding, especially before TPTB got really tight-fisted about what could and couldn't go in licensed fiction; meanwhile, pick up a Voyager numbered novel and you're almost certain to have a bad time) BUT THAT IS NOT A HARD AND FAST RULE. For example, Andrew Robinson's A Stitch in Time (DS9 #27) is widely regarded to be one of the best Trek books ever written, and I would love to second that opinion but unfortunately I can't get my hands on a physical copy for less than $100 and don't read ebooks, so I'll continue to pine.
A key component to enjoying numbered novels is to read them out of order. Jump series. Fuck around. Find an author you like and follow them through their tie-in lit career and lose your mind because you can't talk about how good these books are because no one in your circle of friends knows what the hell you're talking about.
Some personal favorites to get you started: Uhura's Song by Janet Kagan (TOS #21), The Three-Minute Universe by Barbara Paul (TOS #41), Doctor's Orders by Diane Duane (TOS #50), Q-in-Law by Peter David (TNG #18), Emissary by J.M. Dillard (DS9 #1--YES the novelization of the pilot, YES it's just as good), and literally anything by Vonda McIntyre (the Star Trek II-IV novelizations are my favorite, but TOS #2: Entropy Effect is also awesome).
Unnumbered novels can be set pre-, post-, or firmly during canon (or sometimes all 3). Sometimes they are standalone, sometimes they are trilogies or duologies, sometimes they're co-written by William Shatner and you have a great time poking fun at his very specific vision of Kirk (read the Odyssey trilogy, I beg you, it's ridiculous and so fun). Similar to the numbered line, TOS has the most titles, then TNG, DS9, and VOY. Some personal favorites are the Millennium trilogy (DS9), the Legacies trilogy (TOS), String Theory: Cohesion (VOY), Section 31: Shadow (VOY), Imzadi (TNG), The Captain's Oath (TOS), and Revenant (DS9).
If you're more of a post-canon enjoyer, the relaunch novels are your friend. These began with S.D. Perry's Avatar duology in 2001 and stretched all the way to the Coda trilogy in 2021. There is a totally awesome and overwhelming flowchart to guide you through it (be sure to click the image to enlarge), though you will not -- and I cannot stress this enough -- be able to read it all. I've been working on this sucker for 7 years and I've only barely scratched the surface. Pretty much every Trek series pre-DISCO gets pulled into the mix at one point or another, and there are an ungodly number of crossovers, but TNG, DS9, and VOY all have individual offshoots that occasionally weave in and out of each other (the Destiny trilogy, for example, is a bonkers-ambitious ENT/TOS/TNG/DS9/VOY crossover that does a lot of stuff you might hate and a lot of stuff you might love). I highly recommend starting with the DS9 novels as they, in my humble opinion, are the shining star of the relaunch 'verse.
Modern Trek lit functions quite differently from the 80s/90s lit and entirely differently from the relaunch novels; for one thing, the mass market paperback has died an undignified death (RIP) and there's Canon to contend with once more. Furthermore, we're in a weird pop-cultural late-stage capitalism space where things that were once firmly viewed as "beta canon" are being treated as essential pieces of Canon despite them requiring a significantly larger amount of time and money to invest in. I shan't dispense an opinion on that because that's not what I'm here to talk about, it's just an interesting bit of context.
Tl;dr, Trek novels these days are a different beast. Still quite fun though.
Beginning with the 2020 PIC novel The Last Best Hope by Una McCormack, the post-canon litverse "reset" to adhere to onscreen events. Despite the vibe shift, I have quite enjoyed the books I've read in this new era of Trek lit. I've mainly focused on PIC and SNW and really haven't read a bad novel from any of them. Of PIC, Second Self and Rogue Elements were my favorites; of SNW, Asylum by Una McCormack holds my whole heart, but really all four have been awesome (Ring of Fire does stray into s3 territory, so if you are as tired of the Chock/La'ock stuff as I am, beware) (still didn't detract from my overall enjoyment that much though). The Lower Decks tie-in fiction is exclusively comics/graphic novels and I cannot recommend them highly enough. SO damn fun. (Comics are a bitch to navigate but the trade paperbacks linked here and here are easy entry points.)
I have not read many DISCO novels, but The Enterprise War by John Jackson Miller was a wonderful prelude to SNW s1 and Desperate Hours by David Mack was a fun DISCO/SNW crossover. (The DISCO novels are a fascinating microcosm of the shift from beta to semi-prime canon and as a result occupy a strangely liminal space that's really fun if you like to see what happens when established canon knocks up against still-forming canon before the tectonic plates have settled in place.)
ALL OF THAT TO SAY, for everyone there is a Star Trek novel and for every Star Trek novel there is someone. You can wade as deep as you want or hang out in the shallows, it is totally up to you. I've been reading these books for 16 years and still haven't gotten to some of the most famous, but that's just part of the pleasure. Some resources I have relied on heavily in my endeavors are:
Memory Alpha's novel index
The Relaunch Novelverse Flowchart
Trekcore and Memory Alpha (for upcoming publications)