I need help please

I want to buy a decent travel compact camera

My main needs are

fast shoot (I have a baby & right now my old camera takes so long to click she has moved by the time I get the shot)
compact will be easy to slip in coat pocket or bag ]
decent price
HD movie shoot

(I have been checking out the Nikon Coolpix p7700, Fuji Finepix F770 or F500 and the Canon Powershot SX260)

Not sure how much to spend & whether the extra 100 difference on some models is worth the money or the older version will give me just as good shots.

I want to be able to take photos indoors & out

Advice much appreciated thank you xx