Needed to make a note of this again for a client as I'd forgotten since the last account I set up.
Twitter icon (replaces egg) - needs to be square and ideally 400 x 400 (can crop it when you add it)
Header (only seen on your own page) - ideally 1500 x 500 with no gradient colour, as – ignoring any pre-processing you've already done – Twitter will compress the snot out of it anyway when you upload it.
Interestingly, for pictures you want to include in the twit-stream, they need to be no more than 440 x 220 with a ratio 2:1 (info from this Postcron piece).