I already got the "The Beginning" (1963-64) box with "An Unearthly Child", "The Daleks" and "The Edge of Destruction".

I also ordered "The Time Warrior" (1973, introduction of Sarah Jane Smith), "Robot" (1974, introduction of the Fourth Doctor Tom Baker) and "Genesis of the Daleks" (1975, also with SJS and TB).

I can't stand the new Doctor Who, but used to watch the classic episodes all the time when I was a kid.

One of my favourites was Tomb of the Cybermen. 

Quoting klandersen:

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Almost anything from the Jon Pertwee era. Especially the Dalek stories, The Demons and one of my faves which some may think is silly The Three Doctors

Daemons isn't released yet, same with Day of the Daleks and Death to the Daleks... quite a few Pertwee eps needed specific restoration techniques so are coming a bit late to the party. Planet of the Daleks is only just out and has had the surviving b/w episode recoloured amazingly well.

Recommendations? Well it will depend on which actors palying the Doctor you like I think; some like klandersen are Petwee fans... the last 10 years though has seen a strong backlash against Pertween and criticise him for being rude and condescending too often (and of course he rarely leaves Earth so that limits the type of story). I'm not a big fan of Davison's 'softer' style but others can't get enough of him... etc.

My 'top choices' personally, for those released, would be:

The Talons of Weng-Chiang (a masterpiece; just try to suspend disbelief for the giant rat)
Pyramids of Mars (voted most wanted DVD in a poll to get it released)
Deadly Assassin
Robots of Death (though this was an early release without quite the finesse and features of the later ones... it may get a re-release as a special at some time in the future)
City of Death (lovely Douglas Adams humour and great documentary featurette, but isn't in the Key to Time season as klandersen thought BTW)

and loads of other Tom's - anything from the Baker/Hinchcliffe era is going to be good IMO.

Non Tom Bakers:
The Beneath the Surface set is good for Silurians (restored to colour) and the magnificent Sea Devils... Warriors of the Deep not so hot though!
Dalek Invasion of Earth for Hartnell, Seeds of Death for Troughton, Inferno and Carnival of Monsters for Pertwee, Earthshock and Caves of Andozani for Davison, Vengeance on Varos or Mark of the Rani are probably Baker2's best and for McCoy probably Curse of Fenric (the DVD has the original and re-cut as originally planned with new SFX versions) or Remembrance of the Daleks if you like Daleks... going up stairs in the original series!

My favourites:

William Hartnell era:
- The Dalek Invasion of Earth
- The Time Meddler


Patrick Troughton era:
- The Tomb of the Cybermen
- The Invasion
- The Seeds of Death
- The War Games

Jon Pertwee era:
- Inferno
- The Three Doctors
- The Time Warrior

Tom Baker era:
- Genesis of the Daleks
- Pyramids of Mars
- The Talons of Weng-Chiang
- The Deadly Assassin
-The Invasion of Time

Peter Davison era:
- Earthshock
- The Black Guardian Triolgy
- The Five Doctors
- The Caves of Androzani

Colin Baker era:
- Attack of the Cybermen

Sylvester McCoy era:
- Remembrance of the Daleks
- Ghost Light
- The Curse of Fenric

Quoting Kinoniki:

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Quoting DJ Doena:

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I already got the "The Beginning" (1963-64) box with "An Unearthly Child", "The Daleks" and "The Edge of Destruction".

I'm a die-hard Tennant fan and I've never seen a "classic" Doctor Who episode but today I bought this and also the "New Beginnings" set with Baker/Davison. Well they were on sale, couldn't resist. 

What episodes does it contain?

I quite like the Comic Relief episode The Curse of Fatal Death (with Rowan Atkinson as The Doctor for the majority), which afaik isn't available on DVD.

Also, many people don't realise it, but Spoiler:  (Select to view)
makes a sly nod to the series.