Despite just one series this is still not an easy choice. I feel that the first series hit the nail on the head with how Doctor Who should feel...perhaps with the odd dialling down with some of the domestics.
The Unquiet Dead was a lovely episode, an absolute gem as others have quite rightly stated. For a long time it was the only Mark Gatiss script I thought was really stand-out, though he has since rebounded with the excellent The Crimson Horror and the wonderful An Adventure in Space and Time.
Aliens of London/World War Three is another decent story, which many would disagree with. But aside from the farting gags and the awkward cgi-prosthetic Slitheen transitions I felt there was a very cool story under it all...aliens faking alien invasions, it felt very original for the show.
Dalek was another absolute hit, a true classic. It did exactly what it needed to and put the Daleks front and centre of the bad guy roster for the show, and of course a whole new younger audience who perhaps had not seen Daleks before.
The Empty Child/The Doctor Dances was yet another classic. I love this story to pieces and it's nice to see a slower paced story from Moffat who now churns out 45 minute finales and intense epics of timey-wimey proportions. Not to say I don't like a lot of what he does now, but I think his better ideas were back here.
Boom Town was a wonderful calm-before-the-storm type episode and Annette Badland was absolutely brilliant as Margaret in this. We don't get episodes like this any more - they'll never be the one that most people regard as their favourite, but they're the ones that deserve and get a special mention because they do something a little more poignant than usual. The episode ultimately boils down to a conversation in a restaurant (in Cardiff!) but what a conversation it was. It was great to explore The Doctor's morals and the consequences he usually runs from.
But for me, the best Eccleston story has to be the series finale. Largely down to The Parting of the Ways, Bad Wolf isn't without merit. The opening episode has the wonderfully creepy 'Controller' character at the heart of it all, and the trashy games are fun and tense in good measure. Then the story ups the ante in part two with what I consider to be the best Dalek story we've yet seen in the revival. Nine's exit was dignified and emotional without being too drawn out, and Rose's iconic Bad Wolf stuff was so vital that it became part of her return in Series 4 and was again part of the show for its 50th Anniversary. The episodes also mark the first named reference to Torchwood and also introduce Captain Jack's immortality - there's a lot here that makes this a defining story of Doctor Who and it still stands up well now as a gripping two episodes.