There are a lot of early Big Finishes on Spotify, so they're obviously a good place to start for a taster. I'll be doing this after I've finished all the novels. I've also noted down a few recommendations from here and Ganymede & Titan:
There are some quite good Tom audios: The Foe from the Future for Hinchcliffe-style horror, The Auntie Matter for Williams-style fun, The Paradox Planet/Legacy of Death and The Trouble with Drax for something more Douglas Adams-esque, The Skin of the Sleek/The Thief Who Stole Time for something more Season 18.
Anything by Rob Shearman
Dalek Empire
Spare Parts, Jubilee, Doctor Who and the Pirates, Psychodrome, Whispers of Terror and City of Spires/Wreck of the Titan/Legend of the Cybermen are all good.
Anyway(!), yeah – re. Big Finish: I’d recommend the Klein trilogy (A Thousand Tiny Wings, Survival of the Fittest and The Architects of History) as essential listening.
I always hear really good things about the Jago & Litefoot spinoff.
I'll probably be listening to all the Eighth Doctors in order, too, because even though I'll have been through 70+ novels featuring him by that point, it'll be nice to actually hear McGann in the role. There are plenty to go at there.
Monthly AdventuresStorm Warning
Sword of Orion
The Stones of Venice
Minuet in Hell
Invaders from Mars
The Chimes of Midnight
Seasons of Fear
Embrace the Darkness
The Time of the Daleks [part of the Dalek Empire series - probably worth listening to other volumes]
Neverland
[Zagreus - multi-Doctor story featuring 3, 5, 6, 7 and 8. And probably a cardboard cutout of 4]
Scherzo
The Creed of the Kromon
The Natural History of Fear
The Twilight Kingdom
Faith Stealer
The Last
Caerdroia
The Next Life
Terror Firma
Scaredy Cat
Other Lives
Time Works
Something Inside
Memory Lane
Absolution
EDA Series 1The Blood of the Daleks [pt 1 & 2]
Horror of Glam Rock
Immortal Beloved
Phobos
No More Lies
Human Resources [pt 1 & 2]
EDA Series 2Dead London
Max Warp
Brave New Town
The Skull of Sobek
Grand Theft Cosmos
The Zygon Who Fell to Earth
Sisters of the Flame / Vengeance of Morbius
EDA Series 3Orbis
Hothouse
The Beast of Orlok
Wirrn Dawn
The Scapegoat
The Cannibalists
The Eight Truths / Worldwide Web
EDA Series 4Death in Blackpool
Situation Vacant
Nevermore
The Book of Kells
Deimos / The Resurrection of Mars
Relative Dimensions
Prisoner of the Sun
Lucie Miller / To the Death
Dark EyesDark Eyes 1
Dark Eyes 2
Dark Eyes 3
Dark Eyes 4
Doom CoalitionDoom Coalition 1
Doom Coalition 2
Doom Coalition 3
Doom Coalition 4
RavenousRavenous 1
Ravenous 2-4 [forthcoming]
The Eighth Doctor: The Time WarSeries 1
Series 2
Series 3-4 [forthcoming]
Various other bits:
Classic Doctors, New MonstersThe Sontaran Oreal
Day of the Vasha Nerada
Destiny of the DoctorEnemy Aliens
The Diary of River SongThe Rulers of the Universe
That's really quite a long list, isn't it?