Warning, I went off on a tangent.
If you want some good times then the old series is incredibly cheesey fun. Some of the Doctor's are better than others. Second Doctor was kind of meh from memory, stuff with the First Doctor is really old a beat up and some episodes are lost forever (BBC had a fire in their archives) but the First Doctor is a cranky old bastard which makes for hilarious good times because one of the longest running successful television serials started its run with a 60+ year old man yelling at everyone. Third Doctor brings back cranky old bastard again but John Pertwee is far more likable than I found William Hartnell (Again, First Doctor is a really cranky old bastard which is awesome, but not really likable). Tom Baker (Fourth Doctor) runs are of course absolutely timeless classics, still probably the best (although new series has some amazing episodes! The Library is great).
Fifth and Sixth Doctors are both functional but kind of let downs after Tom Baker, not much they could really do about that, certainly admirable efforts on their parts (not going to knock these two actors! Both did good jobs, but Tom Baker was... a little TO into the role to be honest and kind of owned it for his 7 years in it). Seventh Doctor is wow completely different. Sylvester McCoy on the series when it finally tanked and in no part because of him (Shitty scripts and just everything behind the scenes going all kinds of fucked pretty much), the guy did an amazing job and honestly is worth checking out in his other things, technically longest running Doctor although only actually was active in the role for 3 years. Good stuff kind of more nonsense than the older doctors, but his time the role has definitely stuck. Series is better watching it now than it was at the time apparently.
New stuff! Eighth doctor does not exist. Ninth Doctor, Christopher Eccleston was good and at the time seemed to be showing a lot of promise for the new Doctor, then he stopped and we got David Tennant. David Tennant may be a better Doctor than Tom Baker (I think I need to rewatch some Baker stuff) but regardless of how good Tennant is as a character, this is the best the show has ever been. Great scripts, huge budgets and the production value just shows. It is a lot of fun if you can get into it.
Personally I consider it a series you could pick up anywhere of and probably have a lot of fun and there is nearly an endless amount of it you can pick up. The new stuff is great and doesn't rely on the old series at all to be good, but if you do get into the retro stuff the new series is even more rewarding.
Torchwood is a bit more GRIMDARKREALISM but yeah probably gets a few more gags in there as well. Worth your time if you are a fan of the main series I think but I wouldn't really watch it on its own.
YOU MISSED SARAH JANE ADVENTURES. Doctor Who for kids, this is actually pretty cool and there is even cross over between this and the main series. Premise is one of the companions of the Third and Fourth Doctors went back to her regular time on Earth after PAN DIMENSIONAL SUPER PIMP ADVENTURES and is kind of bored. She has some of the tech from her adventures with the Doctor and a robotic dog helper from the old series. They fight crime. Well more they have much smaller scale stuff dealing with aliens and time travel stuff and pretty much you Doctor Who stuff on a much smaller scale and a tad less THE ENTIRE SPACE TIME CONTINUUM IS GOING TO BE EATEN BY A SPACE BEETLE AND THE SPACE BEETLE WAS MADE BY THE DALEKS WHO HATE THE SPACE BEETLE and more kid friendly plots as Sarah Jane is helped by the local kids. So it is kind of Neighbourhood Watch for Space Aliens. My favourite part is that it is the same Actress that has always played Sarah Jane, kept the role since the 1960's.
Oh yeah have I hyped The Master enough before yet? Doctor Who is where The Master comes from and The Master is the best thing ever. Suffice to say Doctor Who has the Grefter seal of this shit is fucking fun.
Edit - Oh yeah and I can't hype the Family episodes enough. That shit is just fucking WOW. Tennant showing probably more range than the other Doctors have ever had the chance to in the role.
