I really don't feel like I'm in the loop here or like I even belong in this thread--the only seasons I've seen are with Nine and Ten!
Then it's time to fill you in, my good friend, it's TIME to fill YOU IN!!! :: Let's all help out on this, as I'll most likely forget some.
Starting with the 1st Doctor, William Hartnell.
The Doctor is a renegade time-lord, exiled from his own planet, by his own people. He fleed his home planet with his granddaughter, Susan and they spent a good while on Earth, until two of Susan's high-school teachers got suspicious of her awesome knowledge, so they followed her after school one day, into a junk yard - eventually Ian and... that chick whose name I can't remember.. ended up on the Doctor's ship, the TARDIS (Time And Relative Dimensions In Space) The Doctor, being a man of science, set the TARDIS in motion with these two new passengers aboard, much to Susan's dismay - Back then the when and where of the TARDIS's next destination was completely random, as the Doctor had intentionally broken the guiding circuits so as not to be tracked by his own people.
As their adventures continue, the meet many kinds of aliens; daleks, cybermen, etc... and with the meeting of the Cybermen ("The Tenth Planet" - Episdoes which have unfortunately been lost) the 1st Doctor grows weary, and is no longer able to live, collapsing to the floor, and to everyones surprise, he re-generates into an entirely new body. (Susan is no longer there at this point, as the Doctor left her stranded on Earth in the year... 2005, I think it was)
There's not much to say about the second Doctor other than that his best story was probably "Tomb of the Cybermen" and also, his last story "The War Games" he is put on trial for his "Crimes against the Time-Lords" is found guilty, this time forced to regenerate, and banished to Earth for 100 years. (Hence the majority of Jon Pertwee's stories being set on Earth) *Phew* this is a really daunting task...
Maybe just go here instead
You can also find out quite a lot here, so long as you're willing to poke around a fair bit.
The 40th anniversary book should also bring you up to speed.
There's also lots of fan sites out there, and I even once came across a "dalek time line" and a "cybermen time line" focusing only on the stories with those adversaries.
and welcome to Doctor Who fandom. ___ happy reading, viewing and researching.