VNA Story arcs

Let's see...

The Timewyrm story arc is fairly easy since it's indicated on the cover, so read Genesys, Exodus, Apocalypse and Revelation for the whole story.

Time's Crucible, Warhead and Witch Mark are much the same and form the Cat's Cradle trilogy. These in turn spark off the Infected TARDIS arc that's middling in the background of every story up to Deceit.

The Future History Cycle begins in Love and War and runs straight through until Lucifer Rising. It's considered by many to be the collection that firmly established the Virgin range's take on the future (i.e. that there was a largely definitive view that authors could each draw from, rather than creating it from scratch).

The Alternate History Cycle begins in Blood Heat and runs through The Dimension Riders, The Left-Handed Hummingbird, Conundrum and No Future.

The Psi-Powers arc is a little bit tricky because it's a lot like the Fenric arc that was initially developed on television. It was a connection between stories that appears more as an afterthought than as something that intrinsically ties each novel together. The progression in its entirety is as follows: Warchild, SLEEPY, Christmas on a Rational Planet, Cold Fusion, The Death of Art, Damaged Goods and So Vile a Sin. However, if you want to see the Psi-Powers Arc from the perspective of the villains it's been recommended to read: Death of Art, Damaged Goods, Sleepy and So Vile A Sin in that order.

There's a final informal arc which can be regarded as a farewell to the trappings of the New Adventures as a whole in The Room with No Doors (which completes the Seventh Doctor's character arc stretching across the range), Lungbarrow (which answers the question of the Other and Ancient Gallifrey) and The Dying Days (which, using Benny and other elements, passes the torch to new projects).

Just read Dimension Riders through No Future in January (having read Blood Heat a while back) and I have to say it's a pretty good arc. I rather wish I didn't know everything about it going in, but I would recommend it.

There were a few references I didn't recognize from earlier VNAs but only Love and War is really necessary and I've heard the audio twice (although there was a paragraph in either Riders or Hummingbird that spoiled Deceit for me).

There's also the lesser mentioned "trying to take a holiday" arc, White Darkness, Birthright and Iceberg.