Not recommended.

This one takes a little while to get going; it has some very cool ideas at play, but most of these are presented in the context of a fairly clichéd narrative in the vein of The Krotons, Full Circle, State of Decay, Paradise Towers, and many other TV stories of that mould, and while something like Paradise Towers knows what its strengths are and plays fully to them in a pretty focused 4-part serial, Timewyrm Apocalypse fills out its lengthy pagecount with flavour and detail of story beats and world details we've seen play out many times before, leaving most of the interesting stuff for the very beginning and very end; in this regard, one recalls Full Circle, one of the blander season 18 serials, bogged down by its familiar concepts. And yet, another thing Apocalypse has in common with Full Circle is the fact it is a perfectly okay story, so even though I couldn't recommend seeking this one out, it has its place as a piece of the early evolution of the VNAs.

It's inoffensive. And perhaps that's its greatest weakness.

Essential background: None
Extensive background: The Power of the Daleks (season 4), the War Games (season 6), Logopolis (season 18), Timewyrm: Exodus (VNA #2)

In my reviews, particularly of the Virgin New Adventures, I prefer to use a 4-tier system of grading:
Essential reading - If you want to read all the best VNAs, get all the most memorable story arc beats, and generally enjoy the VNAs without having to trudge through the mediocre/bad books, or perhaps even if you just want to pick up a good Doctor Who book with no intention of reading the entire series, look for this rating.
Worthwhile for extensive reading - Not outstanding, but I won't outright tell you to skip it if you want a sense of the VNAs overall. If you're determind to only read the best, skip these, but for a read-through of the series, I wouldn't skip them. They're the worthwhile, good-but-not-amazing books. You'll get a stronger sense of character arcs, story arc beats, and the growth of the VNAs as a range if you read these, but it will also take you a lot longer.
Not recommended - Not very good. If you really want to maximise your experience of the VNAs, you could read this, but it's definitely not advised.
Avoid at all costs - An irredeemable lump of human fecal matter. Do not waste your time with this insult to the franchise.

In addition, I list Recommended background that you may find necessary for understanding the story in full, as well as Extensive background for some additional details you may find interesting.