Most "big show" cars have the chutes on the right just ahead of the front hoop of the cage so that you can do as Bruce suggests--back of your hand against the hoop, slide it down and push forward on the chute levers and then tug on the brake lever. Fuel shut off is generally on the left and most funny cars have the fire bottle lever on the brake handle.
In my cars with auto transmissions (and foot brakes) I generally mount the shifter on the right and the chute lever on the left.
This is Brendan Murry's NT/F car that I built a few years back. As you can see, when the chute levers are pushed forward your hand is right in line with the brake lever. As with a funny car the fire bottle lever is on the brake.
Roo