Depends on your tastes really, but below is a brief description of each story to help you decide:-
The Aztecs - Barbara (1st Doctor companion) is mistaken for a god, and they spend most of the story trying not to change history
The Dalek Invasion of Earth - Ever wanted to see a dalek come out of the water? This is the one for you then, it's the Daleks invade Earth with an intent of replacing the planets magnetic core.
The Tomb of The Cybermen - an archaelogy trip to the cybermen's adopted home planet telos - where they find that they're not as dead as their supposed to be.
The Mind Robber - Set in the land of fiction, this is a stretch to the imagination but is one of my favourite 2nd Doctor stories
The Seeds Of Death - Ice Warriors, T-Mats and lots of foam.
Spearhead From Space - 3rd Doctors first story, that features the Autons (yes like the ones in Rose), and quite a good place to start.
Claws Of Axos - pshycadelic nonsense, with bad incedental music - has the Master in.
The Three Doctors - The 1st, 2nd and 3rd Doctor together to defeat an antimatter creature, plus the normal banter with the Doctor and the Brigadier, what more could you want?
Carnival Of Monsters - If you want to watch a story set on a ship stuck in a time loop that's inside a time-scope then get the DVD, never watch the UKTVgold repeat or get the video, as the video is an accidently transmitted version that has an extended cliffhanger, but a jumbled up episode 2 and 3
The Green Death - Giant maggots, meglomaniac computer, one of my favourite 3rd Doctor adventures.
The Ark in Space - It's an ark in space funnily enough, containing the survivors of Earth - but the ark is threatened by the Wirrn
Pyramids of Mars - Has one of the best DVD extras ever in Oh! Mummy, and the story is a classic 4th Doctor one, about Sutekh the Destroyer (an Osiran) and has Sarah-Jane-Smith in.
The Robots of Death - Like killer robots and stories where the Doctor and his Companion are accused of Murder? Then you'll like this one.
The Talons of Weng-Chiang: - Reputated to be one of the best Doctor Who stories, Talons is a must with some excellent supporting characters.
Horror Of Fang Rock - The 4th Doctor and Leela end up at a lighthouse where people are being killed in strange circumstances (trouble is the monster looks like a cabbage)
The Leisure Hive - The 4th Doctor and Romana visit this torist location, after a pretty pointless but fun scene on Brighton Beach. There's one character (Pangol) that can be annoying in this, but it is generally about the ongoing feud between the Fomasi and the people in the leisure hive, plus Pangols mad scheme.
The City Of Death - I'll be getting this as soon as it comes out. The Doctor and Romana are brilliant here, and the story stands up so firmly. Like HHGTTG (original radio/tv series)? Because, this story was written under a pseynedodeum, this story was co-authoured by Douglas Adams himself.
The Visitation - The 5th Doctor, Nyssa, Tegan, and Adric end up in the location where heathrow will eventually be built and then find some aliens who are trying to speed up the plague (also reveals who or what caused the fire of london).
Earthshock - Cyberman story where they try to crash a freighter in to Earth, with a suprising ending.
The Five Doctors - well the 4 and a bit doctors, Tom Baker only appears as footage from the cancelled Shada. The Doctors on the Death Zone on Gallifrey need to work out who sent them there and why.
Resurrection Of The Daleks - The Daleks try to get their creator Davros back, the beggining of the two different factions of Daleks.
The Caves of Androzani - renowned as one of the best Doctor Who stories Caves has a lot of different aspects - with the Doctor rushing against time and pain to save his companion, plus there's the gun runners and sharaz-jeks scheme. Probably the one I'd reccomend over nearly all the others.
Vengeance on Varos - One of The 6th Doctor's better stories, this has a reputation of one of the most violent who stories, but one of the best cliff-hangers for a long time. It's message is to show how violence is wrong which is why there's a lot of violence in it.
The Two Doctors - The 2nd Doctor and the 6th Doctor unite for an adventure in Spain - this story has some very humorous moments, and having Peri and Jamie as the companions works brilliantly. Again, is very violent - but that's to do with the Androgums who like to eat anything. The main plot line is that something is trying to get thier hands on time lord technology.
Revelation of the Daleks - Fun romp with silly scenes, and Daleks & Davros of course - a story thats main premise seems to be Davros wanting to humiliate the Doctor.
Rememberance of the Daleks - The 7th Doctor's on one of his master plan's and the two dalek factions battle it out for the hand of Omega.
The Curse of Fenric - Has a special edition with cgi on the second disc, and a 5.1 track. One of the best 7th Doctor stories, this shows people turning into monsters and Fenric and the haemavores - shows us insight into yet more of Ace's past.
Ghost Light - Not the best place to start, would beffudle you, no matter how hard I try this is the only Doctor Who story I can't say anything nice about.
The Movie - This american production is OK, and it's the only way you'll get to see the 8th Doctor - though you'd probably be better off listening to the BIGFinish audios on BBC7 (Unless you want to see the Doctor kiss someone, a Master who is completely out of character and under 90 mins long).
Dalek Films Boxset - The Peter cushing films are not considered canon but still make reasonable viewing, compared to the originals of the stories, these are far superior in every respect apart from the TARDIS crew themselves.
Doctor Who Dalek Collectors Edition (WHsmith Exclusive) - The best way to buy Remembrance of the Daleks, Ressurrection of the Daleks, and Dalek Invasion Of Earth - I picked this up for £12 in a local smiths (not sure how easily you'll find it now though)
Lost in time - a collection of odd episodes scattered in the archive that would make more sense if you've read the novelisations or have information about the stories.