You'll find plenty of info (and spoilers!) at
http://tardis.wikia.com - the show's been running since 1963 and has three ongoing spin-offs (Sarah Jane Adventures, Torchwood, and K-9) so there's a lot of material in the archive. Some of the 1960s episodes of Doctor Who you'll never see though - the BBC wiped them in the days before video recorders and multi-channel TV were available.
There was 26 seasons from 1963 to 1989, a TV movie in 1996, and then four modern seasons in 2005-2008, then a few stand alone episodes in 2009 before series 5 last year. The start of modern series 5 is a good jump on point, as that's just after the Doctor regenerated into his 11th body, and is when he meets his current companions.