We already had one for the Revival, so why not one for Classic? You got 3 Votes, use them wisely! 
(No counting The Five Doctors, since it’s a bit debatable if it really counts as a Cybermen Story, at least to me )
I just absolutely adore the cybermen design in Tenth Planet. Too creepy and too real. Upsetting and unsettling. Perfect.
In reverse order…
Earthshock: A legitimate classic. A shock to see the Cybermen back for the first time in nearly a decade. Atmospheric stuff in the caves and a full on base under seige in space. Plus… THAT ending!
The Tenth Planet: I quite agree with @mvancore. The true mark of how good that design was is the fact it was revisited again, 50+ years later in World Enough and Time / The Doctor Falls and was utterly chilling. The concept stripped bare… and it’s never been more effective. Plus, it’s a rollicking good story.
The Invasion: This one comes out on top for me. I love pretty much everything about it. Many of my favourite elements are present, including plenty of atmospheric mystery and the Doctor in investigative mode. We see the template (now largely fleshed out from the bare bones last seen in The Web of Fear) for the future Pertwee/UNIT era. Oh, and I do love a good villain. Vaughan is an absolute delight (along with his hapless henchman, Packer). The cybermen themselves actually really benefit from being in the shadows for a lot of the runtime. They cast a dark (yet silvery) cybernetic shadow over the story, and their emergence from the sewers is rightly one of the iconic scenes from the whole of Doctor Who (so good, they copied it to lesser effect in Dark Water / Death in Heaven). I love this story to bits. 
Silver Nemesis is very silly but I like it a lot. So there.
The Invasion is actually genuinely really good, echoing what @realdoctor said above!
Earthshock is also just really good. Full stop.
Voted for the only one I’ve seen so far Attack of the Cybermen.
While I have also voted for Attack and the Tenth Planet, only one of these stories is truly excellent!
Earthshock, Tomb of the Cybermen and Silver Nemesis for me - the first is one of the all-time best classic serials, the second is a really good and atmospheric Troughton serial, and the third is enormously silly but also enormously fun, and a bit of a comfort serial for me.
This poll is making me realise I really don’t like Cyberman stories.
The Invasion is the obvious answer here, it goes on too long but is effortlessly stylish and even pretty scary with some fantastic performances and action.
The only one I haven’t watched here is Earthshock, or should I say haven’t completed because I’ve started watching Earthshock about five times and have given up around the halfway point each time.
I’m sort of cheating because I’ve only seen 5/9 of these, but I really like Silver Nemesis and Earthshock! Only using 2 of my votes so that I can leave one for what might become a favourite when I’ve watched them all. The Tenth Planet seems like one that might be a favourite when I do get round to watching it.
Earthshock, Invasion, Tomb. Boring picks perhaps but I’ve watched each of those over and over and over. I also love The Moonbase and Tenth Planet, and have a real soft spot for Revenge! (HARRY SULLIVAN IS AN IMBECIIIIILE)
Earthshock, Tenth Planet, and Attack of the Cybermen for me–Earthshock and Tenth Planet are some of the best classic stories and I love them dearly, and Attack of the Cybermen is one of my favorite Sixth Doctor serials.
A bit shocked to see Earthshock at the Top, I must admit. I mean I’d like it (even voted for it), but still pretty surprised to see it take the lead with 17% more than Tomb for example.
Anyway, glad to see Tomb and Invasion being so high as well (The Invasion deserves the Number One spot-)
I love the cybermen so this was kinda challenging.
But the Invasion and Tomb of the Cybermen are first rate. Earthshock is to but I cry every time I see it. 
Like a certain Cyberleader would say.. an EXCELLENT Taste in Choices 
The Tomb of the Cybermen is perhaps the best (objectively?) but Earthshock is a lot of fun. So is Silver Nemesis!
I’ve never seen (or heard of) Tomb of the Cybermen, so I voted off of the three options I have watched: Earthshock, Attack, and Silver Nemesis. I didn’t care for the Seventh Doctor serial, but I do like ES and AotC.
While I didn’t vote for it, I feel a bit sorry for Wheel in Space. Not a favorite episode, but it introduces Zoe! It deserves something for that.
Tomb (or rather memories of Tomb) forms the basis for Attack. Tomb is where we were initially introduced to Telos.