The original goes back to 1963, so its dated as all get out with the effects. But if you want to know how it all started thats the best way.
I've just seen the modern, so I can't comment on the old one, but you definitely should watch it! Jump in!
The First series from 196(4?) with William Hartnell is good for the sheer historical wossname of it all. Origionally filmed in 405 line black and white, its grainy, white-outed, the sets aren't stable, the Daleks squeak on the studio floor, but its still wonderfully austere and dramatic.
I think the Sylvester McCoy era was the Nadir.
The new stuff is well sexed up. Amy Pond, well, those legs. She'd turn a gay man straight. Trust me. ( I hope the boyfriend doesn't read this ).
Don't bother with the books.