In a nutshell, what the others were hinting at, is that Doctor Who has been around a long time (50 years nearly, 33 on air), and thus it's a bit more complicated than that.
1963 - 89
158 stories ranging from (mostly) 1 to 12 half hour (25min) episodes
First 50 stories are b&w; 10 of which are entirely missing, and 17 partially missing from the archives
7 actors played the Doctor during this original run
1996
First attempted revival
90 minute telemovie produced by BBC/Universal/Fox
7th Doctor reprised his role, then passed on to the 8th
2005 - Present
74 episodes to date (at least 9 more confirmed), mostly stand alone 45 min duration
First 3 seasons recorded in SD; first HD episode "Planet of the Dead" in 2009
3 new Doctors to date
Now plenty of people just ignore the old episodes and go straight to the "NuWho" series, that began in 2005 with the episode "Rose", starring Christopher Eccelston as the Doctor. (Indeed, if you can't handle say, the original 60's Star Trek, don't worry about the original series of Doctor Who; great as it is, I wont even bother trying to push it on you.)
Yes, Doctor Who (2005) didn't go HD until 2009, so the first 4 years are not HD. Suck it up, princess, HD isn't everything.
You could start with Rose, as it was indeed intended to grab newcomers, and give you a basic grounding... Probably the next best option would be "Smith and Jones" (S3E01), which marks the 2nd year for the 10th Doctor - David Tennant. After that... S5E01 The Eleventh Hour - new Doctor again, with Matt Smith, and arguably very popular with the young'uns... (Not sure how old you are, sorry)
If you've not seen any WHO before, and you want to know if it's really any good, I'd recommend "Girl in the Fireplace" (S2E04), or "Vincent and the Doctor" (S5E10), as probably 2 of the best of the new series. (Or a 2 parter - The Empty Child/The Doctor Dances from S01, though it's not intended as an introductory episode.)
(In case you don't know... "the Doctor" is an alien, who has the ability to "regenerate" when his body suffers a normally mortal wound, thus allowing the show to continue after the original actor was forced to retire due to illness. There have now been 11 Doctors, between the original and new series. Unlike say, the two actors who played Darrin in Bewitched, who are similar in appearance, and portray the character near identically, the Doctor's personality and appearance changes with each regeneration, but he retains the same basic ideals and morals...)
If you like it what you see, go ahead and watch from Rose right through... And if you can handle pre-GenX attention spans... To get in an episode from each Doctor, track down:
An Unearthly Child (1963; the very first story - at least watch the first episode, even I'll admit it gets a bit slow after that, but the first 1/2 hr is television history)
The Mind Robber (1969; the most surreal the series ever went)
The Time Warrior (1975; all-time classic and great intro to old Who)
Genesis of the Daleks (1976; origins of the series' biggest bad - The Daleks)
Earthshock (1982; Before Borg, Cybermen were threatening the resistance is futile)
Vengeance on Varos (1985; Forgive him his attire)
Curse of Fenric (1989; trying to be more adult, but it's still really a kid's show)
"The Movie" (1996; biggest budget the show ever had, with a great choice for Doctor, just not the best plot)