Where should I start with...

... Modern Who?

There are a number of jumping-on points with the revived series of Doctor Who. There is, of course, Rose, the very first episode of series 1 starring Christopher Eccleston and Billie Piper. However, there are also two other episodes designed to be episodes that it's easy to start from; The Eleventh Hour and The Pilot, although the former is probably a better place to start as it's a new Doctor and there's very little reliance on continuity in series 5 whilst there's moreso in series 10.

... Classic Who?

Where to start with Classic Who is a more difficult question to answer. There is, of course, the very first episode (An Unearthly Child) but some might find the very slow pace of the early seasons where stories can be as long as twelve episodes, as well as the fact that it's black and white, difficult to deal with. Spearhead from Space, the first story in colour, is a sort of soft reboot of the show with a new Doctor, new companion and new status quo with the Doctor being mostly earthbound.

There are other places to jump onboard, though. The Ribos Operation is the first story in a season-long arc featuring Tom Baker as the Doctor and new Time Lady companion Romana, as well as K9. Remembrance of the Daleks is a very good story featuring a darker Doctor and the first in a run of decent stories that, of the new show, are arguably the most like the new series.

... Big Finish?

If you've watched New Who and aren't familiar with the classic Doctors, a great place to start would be with the Tenth Doctor Adventures, which are pretty good and feature companions and a Doctor well-known to even non-Who fans. However, the Eighth Doctor Adventures was designed to be easily accessible to fans (and non-fans) of New Who, featuring Paul McGann's Doctor in adventures far shorter than most Big Finish stories, with a modern companion and plenty of really good stories. To introduce yourself to other classic Doctors, the Classic Doctors, New Monsters box sets would be a good idea, and there's always the War Doctor series for those who enjoyed John Hurt's incarnation in The Day of the Doctor.

If you are familiar with the classic series and have a favourite classic Doctor, the best place to start might be with your favourite. The Fourth Doctor features almost exclusively in the Fourth Doctor Adventures, in which he travels with Leela and both incarnations of Romana, so the best place to start would be the beginning of any one of his seasons.

For the Fifth Doctor, the best place to start is probably Spare Parts, an excellent story with Nyssa as a companion that greatly inspired Rise of the Cybermen/The Age of Steel. His adventures with Tegan, Nyssa and Adric all together were continued with The Fifth Doctor Box Set, and then in the Main Range with Mistfall.

The Sixth Doctor is far more genial on audio than he was in season 21/22. He gets a new companion, Dr Evelyn Smythe, in The Marian Conspiracy, which is a very good historical story painting a more sympathetic Queen Mary I and beginning a wonderful Doctor-companion relationship that spans a number of good stories. This is probably the best place to start. Alternatively, there is The Sixth Doctor - The Last Adventure which explains the circumstances around the Sixth Doctor's regeneration at the beginning of Time and the Rani. Each of the four stories has a different companion (Constance Clarke, Charley Pollard, Flip Jackson and Mel Bush), which could be seen as a good way to introduce you to these characters before meeting them in the Main Range. It's a matter of preference.

It's somewhat more difficult to find a particular starting point with the Seventh Doctor since he's almost always travelling with Ace. The simplest answer is just to start with his first story, Fearmonger, which just so happens to be one of his best. Following the Doctor and Ace chronologically from that point is probably the best idea.

With the Eighth Doctor, the aforementioned Eighth Doctor Adventures is a good place to start. Alternatively, if you're looking to infiltrate the Main Range, Storm Warning (his very first) is definitely the place to start. The Doctor is reintroduced after the... let's say imperfect film, and we are introduced to his popular companion Charlotte Pollard. The two are delightful in this story and following their adventures from there is advisable. There's also the Dark Eyes 1 box set, although listening to the Eighth Doctor Adventures first does better illuminate the Doctor's mental state and motivation. Lastly, there is The Eighth Doctor: The Time War.