Does the War Doctor series stand on its own?

It's not quite as dark as I hoped it would be, but the series is still very well-written and even better acted.

And yes, it does stand on its own. The War Doctor series was written and produced prior to much of Big Finish's Time War output, so the various connections that have been forged (primarily in the Eighth Doctor range) are retroactive continuity to tie into the characters/plot elements that were established in the War Doctor range. Honestly the only real tie-ins that require any external knowledge are that the War Doctor is a thing (established by TV), and one character from the Fourth Doctor's TV (and subsequently audio) era turns up at one point (that's the best way I can think to write that without spoiling anything).

My advice: go for it. Anything where you can hear John Hurt and Jacqueline Pearce verbally spar is worth it all on its own, but that they're playing Gallifreyans during the Time War makes it even more worth it.

yes, it stands well on its own. BF have since produced a few retrospective prequels featuring some of the characters but the original war doctor series was produced without these

I just finished the whole series a few days ago.
I had held back ages buying the series, because reviews said that they were disappointed that these stories did not go far enough and that it is not dark enough. Many people say these are just straight forward Doctor Who stories.

My opinion after having listened to them all-
better than I expected. Most likely thanks to the awesome cast.
The bickering between Cardinal Olistra and the Doctor is priceless.
I liked the second set, "Infernal Defices" best. The stories do get a bit samey after a while, especially when you listen to them all in one go over only a few days, like I did.
It does get quite dark, but not as dark and evil as the War Master stories get.
The Doctor is still the Doctor, even if he is quite pragmatic and has no problems making hard decisions and killing when necessary.
This makes it more believable than some of the 8th Doctor War stories in my opinion.
There are a few badass scenes, but less than most people expected, I assume (I think this was part of the disappointment for some people).

Are these straight forward Doctor Who stories? Yes and No. They are darker than many Main Range releases (with a few noteable exceptions) and the Doctor is more brutal and willing to kill than most of the time, and he is as rude and grumpy as the 12th Doctor was in series 8 (since the 12th Doctor is my favorite, no problem for me there).
There is indeed less "pew, pew, pew" than you would expect of war stories, but for me, that would get boring and tedious pretty quickly, so I see this as a plus.

For me, the series was totally worth it while on sale.
Personally, I liked the 8th Doctor Time War stories better overall, but I think that comes down to personal taste.

I think the War Doctor series is actually my favourite thing that Big Finish have done.

They’re not all high concept stories and the War Doctor isn’t an absolute bastard, but that’s not the point. Each set gives us a different aspect to the Time War; on the ground combat, high concept weaponary, espionage and the outfall of the War. All of them with a Doctor Who slant on them. They’re not just simple Doctor vs Dalek affairs, we get direct involvement from the Daleks, stories where they’re strategising behind the scenes and a couple where they’re not in it at all.

The War Doctor is the Doctor just trying to do his best in the midst of the Time War. He makes tough decisions and does it ruthlessly and regularly. He’s scarred and weary from centuries of fighting. He’s not all guns blazing, but he doesn’t need to be.

Ollistra makes for a great foil to the Doctor. Their sparring is a highlight of the range and their relationship develops throughout.

The four sets give us an era for the War Doctor and it’s a real coup that John Hurt reprised the role. One of the greats and my favourite actor. It’s an era that feels substantial, yet it’s one that barely scratches the surface of this long and gritty tenure. And that’s exactly how it should be.

To answer your question: yes, the series stands on its own and each set is standalone too. There’s references made to the previous sets later on, and the third leads directly into the fourth, but it’s nothing that requires deep knowledge.

Awesome set of stories, the late John Hurt as the Doctor & Jacqueline Pearce as Cardinal Olistra are both fantastic & as Tulgirl mentioned there bickering is hilarious.

The tone of storytelling is different as the War Doctor may sometimes need to risk the needs of the few to save the many.

12 episodes of tense, terrific drama.

Yes. But I really do feel that the recent 8th doctor audios would have been war doctor ones if hurt was still with us

I understand that feeling -- I get it sometimes too -- but I seem to recall @scotthandcock saying on this forum that that isn't the case. I could be wrong, but I could have sworn he clarified that for us at one point.