Are you going to put the Arduino board in the box ?
You could go for one of the small clone boards, like the Really Bare Bones Board or the Boarduino. This would reduce the size requirements considerably, the LCD would probably be the limiting factor.
As for the buttons, there are so many choises, you could mount them on a small PCB (or Veroboard) behind the frontpanl of your chosen enclosure, or directly in the frontpanel, depending on the type of button you choose. The same goes for the LED's.
Does your camera + other equipment have some kind of power you could tap into? this way you could avoid having seperate batteries for the timer. If such a voltage exists you might have to regulate it down to the voltage required by the Arduino board + LCD. But it would simplify things.
For the enclosure i would try to find soemthing as flat as possible, and from the very start try to find some kind of clamp or other attacment system to mount it on your other equipment. This kind of project frequently ends up, being attached with gaffer tape or something like that, whis in the long run is very annoying.