Like others have already said, it depends on what you want. If you are looking to get into the intereconnected, post TV and movie series relaunches there are several different places that serve as good jumping on points. There's no official names, but I like to refer to the inconnected books as the Novelverse.
TOS: Outside of miniseries the TOS books are pretty much all standalone, so you can pretty much start anywhere. There are a few that connect back to the wider relaunch, so we could probably recommend some of those if that's what you want.
DS9 Relaunch: Either
the Avatar duology, or Twist of Faith, which is an omnibus that collected the Avatar books, and the next novels and one novella.
TNG: There were several books that came out that are connected to the wider Novelverse before them, but the main story arc for the TNG books really starts with the
A Time To... series, which takes place between Insurrection and Nemesis. After Nemesis these books then spun off into the TNG Relaunch and the Titan series, which follows Riker, Troi, and the crew of his new ship the USS Titan. Along with Riker and Troi, there are several other familiar faces, like Tuvok and Melora Pazlar.
Titan: The first Titan novel is
Taking Wing.
Destiny: This was a big crossover trilogy involving characters from every series except TOS. It deals with a massive Borg invasion and is a big status quo changer, so it serves as a really good jumping on point.
Along with Titan there are several other series that focused on their own new casts, which are usually made up of original characters, and guest stars from the different series.
Vanguard: A TOS era series focused on a space station out in an barely explored region of space, and it is amazing. The first novel is
Harbinger. The most prominent familiar face here is M'Benga, but the Enterprise crew and some other characters from the shows and movies do make appearances.
SCE/Corps of Engineers: Follows the crew of a Corps of Engineers starship, was originally released as a series of e-book novellas, but most of them were later collected in paperback omnibuses. The first novella is
The Belly of the Beast, and the first omnibus is
Have Tech, Will Travel. Familiar faces include Scotty in a recurring role, Sonya Gomez, Duffy, Stevens, and Lense. Part way through the series the title changed from SCE to Corps of Engineers.
New Frontier: The first series created just for the novels, it starts with four novellas,
House of Cards is the first. The novellas were later collected in
an omnbius. The familiar faces here are Shelby, Robin Lefler, and Selar.
The Lost Era: This is a series of standalone novels that follow characters from the different series in the time between the TOS movies and TNG. Since they're standalone you can pretty much read any of them at any time.
IKS Gorkon: A series set after DS9 which follows the crew of a Klingon starship, the cast is first introduced in a TNG novel
Diplomatic Implausability.
Stargazer: Follows the early years of Picard's first command before the Enterprise. The cast is introduced in the TNG novel
Reunion. As far as I know Picard is the only familiar face here.