There's only one Doctor Who movie (that's not the weird knock off one) and that's from 1996 (When they last had a crack at reviving Who). It's of the 8th Doctor. I'd say it can be skipped.
As for Torchwood, due to it running alongside Doctor Who it does kinda mesh in with Doctor Who. Captain Jack, who you're about to meet, leads Torchwood and comes back to Doctor Who a few times. I'd say go along lines of:
DW S01, DW S02, TW S01, DW S03, TW S02, DW S04 (then from here you can watch S03 n S04 of Torchwood at any point as it moves on to Moffat's Who and he doesn't have Jack come back again) DW S04.5(the specials, Planet of the Dead/Water of Mars/End of Time.)
The final episode of TW S01 then leads right onto the 3rd from last (it's a three part finale) episode of series 3 Doctor Who, so you could maybe watch both series at the same time.
Also if you got past "World War Three" with the Slitheen (farting aliens) then you've got past the worst of the goofiness and now you pretty much just have cheese. Daleks are considered scary cos this is a kids show. A 50 year running kids show. Many of the kids that watched it n got scared of the Daleks then grew up and became columnists n would write about how the Daleks are shit scary. One of them grew up and thought "you know what's really scary? Statues and gas masks and shadows!" And he was allowed to write for the show. (If at the start of the show it says "By Steven Moffat" you're in for a good episode. He's also the current lead writer of the show and he's planted a lot of stuff very early on.)