Honestly, I’m mostly just going to be echoing a lot of what @nyssaoftraken said, that’s a good list.
I am also a completionist, and a fun thing I’m noticing as I see other people’s reviews is that my enjoyment threshold for these is quite low (I’ve basically enjoyed almost all of them so far), and my standard for what counts as a prerequisite is quite high (there’s lots of callbacks and foreshadowing and interconnectivity that I don’t want to disrupt), so I’m possibly not the best person to ask when it comes to which ones are skippable.
Basically, this site lists all 73 of them, in release order, and I kind of just want to point you there
If you want absolutely everything, there’s also the novelization of the 8th Doctor movie that acts as a book 0. Then there’s The Infinity Doctors, which is deliberately contradictory and unclear about where it fits in the timeline. I personally think the least messy place is between books 1 and 2, but you could realistically put it anywhere in the first half of the series. Wolfsbane is a 4th doctor book, but the 8th doctor shows up and plays a major role, and from his perspective it takes place between Casualties of War and The Turing Test. Lastly, Fear Itself came out after the main series ended, and is set between Earthworld and Vanishing Point.
If, however, you don’t want to read all 77 books, I tried making a pared down list. I was not entirely successful:
The Infinity Doctors (probably controversial as book 1, but I think it works here, and there’s really not a better place for it to go. It’s also skippable if you like)
Vampire Science (not technically plot essential, but extremely popular, and the one everyone recommends starting with)
Genocide (not plot essential, but very popular)
Alien Bodies
Kursaal (not popular, but I quite like it, give it a go, but feel free to skip if it’s not clicking)
Longest Day (not great, only really relevant for about the last chapter)
Dreamstone Moon (not essential, but I quite like it)
Seeing I
The Scarlet Empress (not plot essential, but extremely popular)
Beltempest (not popular, but I quite like it, give it a go, but feel free to skip if it’s not clicking)
The Taint (not great, but it’s the introduction story for a MAJOR character)
Demontage (not at all essential, I just think it’s fun)
Revolution Man (not plot essential, but very popular)
Dominion (not technically essential, but it’s a nice breath of fresh air after a very heavy book)
Unnatural History
Interference: Book 1
Interference: Book 2
The Blue Angel (not plot essential, but extremely popular, you’ll probably want to have read The Scarlet Empress first)
The Taking of Planet 5
Frontier Worlds (not popular, but I quite like it, give it a go, but feel free to skip if it’s not clicking)
Parallel 59 (not popular, but I quite like it, give it a go, but feel free to skip if it’s not clicking)
The Shadows of Avalon
The Fall of Yquatine
Coldheart (not essential, but I quite like it)
The Banquo Legacy (not essential, but I quite like it)
The Ancestor Cell (Finale to the first half of the series, and all the arcs they’ve been doing up to this point)
The Burning (Basically a new pilot, you could very easily just start reading here)
Casualties of War (not essential, but I quite like it)
Wolfsbane (not essential, but I quite like it)
The Turing Test (not plot essential, but extremely popular)
Escape Velocity (not great, but extremely plot relevant)
Earthworld (not plot essential, but very popular)
Fear Itself (not plot essential, but very popular)
Eater of Wasps (not plot essential, but very popular)
The Year of Intelligent Tigers (not plot essential, but the single highest rated EDA according to this site)
The City of the Dead (not plot essential, but extremely popular)
Grimm Reality (not essential, but I quite like it)
The Adventuress of Henrietta Street
Mad Dogs And Englishmen (not plot essential, but extremely popular)
Hope (not essential, but I quite like it)
Anachrophobia (not plot essential, but very popular)
Trading Futures (not essential, but I quite like it)
The Book of the Still (not essential, but I quite like it)
The Crooked World (not plot essential, but very popular)
History 101 (not essential, but I quite like it)
Camera Obscura
Time Zero
and I’m only up to The Domino Effect, so I can’t really comment much past here, but you may have noticed a pattern (they’re good, just read them all if you can. Every pass I made on this list, I added more books, and I still feel bad about a lot of the ones I left out).