For the sensor dust thingy, it'll depend on how lazy you are.
Usually those dust that can be shaken off by the filter can also be
blown away using a blower. If your sensor has dust, it'll end up as
black spots on your pictures.
Generally, all current dSLRs have quick startup. As for anti-shake,
Canon and Nikon are all lens based. Sony's offering has sensor
based, not too sure about other manufacturers.
As for focus, I usually only use one, the middle one. I'll aim at
my subject, focus-lock, then I compose. Only when I'm lazy then
I'll use AiAF (Canon)
Anyway, if you want 1st hand and below 1K, then I'll suggest you
get Nikon, since that is the one that fits your budget. Go clubsnap if you wanna
know more on photography