Pure Random thoughts

Start your companion arc with Pond and the Eleventh Doctor (Season 5 through episode 705, I believe everything is on Netflix), but before that I recommend (can be watched as standalone episodes without knowing those companions): 408, Silence in the Library and 409, Forest of the Dead because they introduce River Song (and she is just a bloody brilliant character) and Blink (310), which, IMHO, is to Doctor Who nearly what Hush was to Buffy.

All those, with a few exceptions, (I'd skip the Venetian vampires, 506 and maybe fast forward through or skip the Silurian two part 508/509, but the bizarre ones about Flesh clones are important 605/606) are written by Steven Moffat, who is A-mazing at character and story building and I just want to have time to watch everything he works on (Sherlock and Coupling, among others).

If you're watching and it starts to not make sense in the greater storyline, check the writer for the episode on imdb or in the opening credits, they throw in a couple one offs (one Really crazy one is Neil Gaiman's, 604) that sometimes don't connect to Moffat's bigger plotline.

There was a BBC America marathon when we first brought LilMunky home and our entire day was quiet time punctuated by bihourly feedings, so since we barely left the room (or slept) we ended up watching several seasons (subtitled with the volume low) and finally understood all our Whovian friends, but there is always a special place in my heart for Pond and Eleven.