A brief guide to the time and space adventures of the Eighth Doctor, and his companion Charlotte Elspeth Pollard, Edwardian Adventuress. 

Eight and Charley’s episodes are one continuous story arc, and should be listened to in chronological order. The unskippable key episodes for their overarching plot are:

1. Storm Warning
2. The Chimes Of Midnight
3. Seasons Of Fear
4. The Time Of The Daleks
5. Neverland
6. Zagreus
7. Scherzo
8. Creed Of The Kromon
9. The Last
10. Caerdroia
11. The Next Life
12. Terror Firma
13. Absolution
14. The Girl Who Never Was

Their complete adventures consist of the following episodes, (approximately) in chronological order: 

Storm Warning

• Notes: Charley’s introduction.
• Standalone? Yes. 
• Essential to the plot? Yes. 

Sword Of Orion

• Notes: Adapted from an Audio Visuals episode.
• Standalone? Yes. 
• Essential to the plot? No.

The Stones Of Venice

• Notes: -
• Standalone? Yes.
• Essential to the plot? No.

Minuet In Hell

• Notes: Adapted from an Audio Visuals episode. Don’t worry about historical errors, they’ll be explained later. 
• Standalone? Yes.
• Essential to the plot? No. Although Charley meeting the Brigadier will become important later, you don’t need to have listened to this episode to understand it. 

The Light At The End

• Notes: The 50th anniversary episode, featuring many Doctors and companions. 
• Standalone? Yes.
• Essential to the plot? No.

Invaders From Mars!

• Notes: Don’t worry about historical errors, they’ll be explained later. 
• Standalone? Yes.
• Essential to the plot? No.

Enemy Aliens

• Notes: Part of the “Destiny Of The Doctor” arc. 
• Standalone? Yes.
• Essential to the plot? No.

The Chimes Of Midnight

• Notes: The most well-loved Eighth Doctor episode ever made. 
• Standalone? Yes, but listening to Storm Warning first is recommended. 
• Essential to the plot? Yes.

Seasons Of Fear

• Notes: Don’t worry about historical errors, they’ll be explained later. 
• Standalone? No.
• Essential to the plot? Yes.

Living Legend

• Notes: Available for free!
• Standalone? Yes.
• Essential to the plot? No.

Letting Go

• Notes: Part of the “Short Trips” range. 
• Standalone? Yes.
• Essential to the plot? No.

Embrace The Darkness

• Notes: -
• Standalone? Yes.
• Essential to the plot? No.

Solitaire

• Notes: A Companion Chronicle.
• Standalone? Yes.
• Essential to the plot? No.

The Time Of The Daleks

• Notes: -
• Standalone? No.
• Essential to the plot? Yes.

Neverland

• Notes: Also consider listening to The Apocalypse Element (Sixth Doctor) if you’d like to hear more of Romana’s backstory.
• Standalone? No. 
• Essential to the plot? Yes.

Zagreus

• Notes: Where to even begin. It’s four hours long. Everyone’s in it. It’s a mythical beast of an episode. If you like, listen to Omega (Fifth Doctor) beforehand for some more background information on Rassilon.
• Standalone? No.
• Essential to the plot? Yes.

Scherzo

• Notes: The beginning of the Divergent Universe arc. There’s nothing wrong with your speakers. (There may be something wrong with Robert Shearman.)
• Standalone? No. 
• Essential to the plot? Yes.

Creed Of The Kromon

• Notes: The introduction of companion C'rizz.
• Standalone? No.
• Essential to the plot? Yes.

The Natural History Of Fear

• Notes: Trigger warning: everything. 
• Standalone? Kind of. If you simply want to experience a mindfuck, go ahead and listen to it as a standalone episode. It is, however, strongly tied of the overarching plot.
• Essential to the plot? If you feel uncomfortable listening to extreme torture, you can skip this, but it’s highly recommended you listen to it. 

The Twilight Kingdom

• Notes: -
• Standalone? Pretty much, but part of the overarching Divergent Universe arc. 
• Essential to the plot? No.

Faith Stealer

• Notes: -
• Standalone? Pretty much, but part of the overarching Divergent Universe arc. 
• Essential to the plot? No, but it does provide strong foreshadowing and character development.

The Last

• Notes: -
• Standalone? Pretty much, but part of the overarching Divergent Universe arc. 
• Essential to the plot? Yes. Although it doesn’t introduce major plot developments, it’s full of important foreshadowing. 

Caerdroia

• Notes: -
• Standalone? No.
• Essential to the plot? Yes.

The Next Life

• Notes: The end of the Divergent Universe arc. Stars Daphne Ashbrook. 
• Standalone? Not even remotely. 
• Essential to the plot? Yes.

Terror Firma

• Notes: -
• Standalone? No, but if you really like Davros and for some reason want to skip the rest, you could potentially listen to it if you’ve only heard Storm Warning.
• Essential to the plot? Yes. 

Scaredy Cat

• Notes: -
• Standalone? Yes.
• Essential to the plot? No.

Other Lives

• Notes: Also works as a fantastic standalone introduction to team Eight, Charley and C'rizz. 
• Standalone? Yes.
• Essential to the plot? No.

Time Works

• Notes: -
• Standalone? Yes.
• Essential to the plot? No.

Something Inside

• Notes: Originally written for the Divergent Universe arc, but postponed. Much of this story deals with gore and extreme torture.
• Standalone? Yes.
• Essential to the plot? No.

Memory Lane

• Notes: Eddie Robson’s first audio!
• Standalone? Yes, but it’s a good idea to have some basic knowledge of who C'rizz is, what he looks like and what his abilities are.
• Essential to the plot? No.

Absolution

• Notes: It’s recommended you listen to at least one of the previous five episodes beforehand, so you can get to know C'rizz a little better.
• Standalone? No.
• Essential to the plot? Yes.

The Girl Who Never Was

• Notes: -
• Standalone? No.
• Essential to the plot? Yes.

And that’s all! From this point on, Charley’s story continues in The Condemned, and Eight begins his second long story arc in Blood Of The Daleks.

Be sure to check out TV Tropes for recaps, and the Doctor Who reference guide for detailed summaries.

Have fun!