I saw a post noting the Hitchhiker's Guide vibes in Wild Blue Yonder, and noticed the replies were full of Doctor Who fans to whom the references were news - fair enough, obviously, Tumblr has a young and international population.
Most Who fans probably know the name Douglas Adams if only vaguely - that this independently successful author was also at once stage in the late 70s Script Editor for Doctor Who and himself wrote three very well-regarded serials for the show.
They may also be aware that he's a particular influence on New Who partly because of that direct connection, and partly because he's kind of to British and/or comedic science fiction what was Tolkein is to fantasy.
So the suggestion you try some Adams if you're a Doctor Who fan is probably not a new idea. But for many, diving into fairly tangentially related fiction from 40+ years ago might not seem very tempting on those grounds alone.
But just in case no one's told you, what Hitchhiker's Guide can offer you as a New Who fan is kind of more New Who.
As I say, though Adams was only briefly (though significantly) in charge of Who itself, his influence on modern Who writing is almost as big on its own as the rest of Classic Who combined.
And it's not just the voice and humour that will ring a bell.
The Hitchhiker's Guide to the Galaxy is what happens when you tell the Doctor Who story but take away the Tardis from the Doctor figure. It's a twist on the Doctor Who format where an alien grabs a human away from Earth to travel through a mad galaxy with them, but this alien has no transport of his own and must thumb a ride, and instead of a Littlest Hobo urge to fix every bad situation he stumbles into wishes only to have a good time (bit of a Hartnell touch there I guess).
Crucially I'm not describing a parody of Doctor Who. I don't now that Adams was even super conscious of this read of his most famous tale. But he had certain archetypes in his brain and the comedy writer's habit of wondering 'what if X but Y' and what you get from it could absolutely be described as the Doctor Who show of a different timeline. Something which offers all the pleasures of Doctor Who approached from a different angle.
Finally, in terms of what format to seek out (because Hitchhiker's exists as a radio serial, a set of novels, a TV series and a much later film adaptation) I'd strongly recommend the radio series. In general, and specifically as having the most of offer Doctor Who fans.
The books have become often regarded as somehow the central 'canon' because people assume as books they must have come first. In fact the radio series came first.
I also think it couldn't be more perfect for Doctor Who fans because like that show it's got all the pleasures of great performances as well as the great writing (there is a Hitchhiker's TV series but trust me when I say this is tale built for audio). It's not just full of great performances delivering Adams' comedy perfectly, it also feels huge; the music and sound design evoking such an existentially big, grand, weird, thrilling universe. So especially if you already like Big Finish stories but haven't listened to Hitchhiker's Guide before, you've got such a Who-ish treat awaiting you.
(Toppodcast dot com has it all available.)