I’ll try and help you out with this one actually!
When it comes to the First, Second, and Third Doctors, you can pretty much start anywhere. The Companion Chronicles are set in between the TV episodes for the most part, so you can listen to any of them without needing context from the other audios.
The Fourth Doctor’s audios tend to follow a general continuity within themselves, so those are best listened to in order, but these are also set in between the TV episodes as well.
For Five through Seven, there are a decent amount with TV companions, and as long as you listen in release order, they should make enough sense on their own. Of course, there are some new companions introduced as well, and my recommendation would be to follow their arcs, since it’s a fresh look with a mix of old and new characters.
For the Fifth Doctor, ‘The Eye of the Scorpion’ introduces Erimem, who travels with Five and Peri.
For the Sixth Doctor, ‘The Marian Conspiracy’ introduces Evelyn Smythe, (a personal favorite of mine) and stays with him for quite awhile. ‘The Crimes of Thomas Brewster’ introduces Flip Jackson, but you could probably start at ‘The Curse of Davros’ and still understand her story easily enough.
For the Seventh Doctor, ’ The Harvest’ introduces Hex, and starts off a very long arc.
For the Eighth Doctor, you can either start at ‘Storm Warning’ with Charley Pollard, or ‘Blood of the Daleks’ with Lucie Miller. Eight is probably the most accessible Big Finish Doctor, since all his companions and stories are brand new.
There are also the spin-offs, which you can listen to at your discretion. Enjoyed Jago and Litefoot in ‘Talons?’ There’s a spin-off for them. Want to know more about Gallifreyan politics? Try ‘Gallifrey.’ Need something cheerful and ridiculous? Iris Wildthyme.
There are some pretty good guides to listening to Big Finish out there, and people will definitely be happy to help you figure it out :)