If You have a choice of colour the dark grey (anthracite) does least harm to boat's look. Not showing dirt and kind of "vanishing" when You look at it from any distance. Please remember, that the netting is definitely not a barier for any dog larger than Chihuahua or Yorkshire terier if one really WANT to jump over it, especially if You do have a teak deck
(fiberglass, even with non slip, is not convenient ground for dog to jump from, claws slip anyway).
Better to keep claws well trimmed, it will be easier and safer for dog to move around - carpeting all the surfaces is not practicable
Sooner or later the dog will learn to negotiate the companionway
. My feeling is it is important decision, how to prepare the companionway
for the dog to be safe. You can cover the steps by the pieces of carpet for example, but this will allow the dog to move swiftly up and down. If You prefer to have better control, You can just cover the floor under the companionway by carpet on the foam base. Even if the dog will go down "cartoon way" it will be not so dangerous, and dog will be very careful on slippery (for him/her) companionway steps.
Of course - the dog should have not an access to the companionway while the boat is under way.
Anyway - I do believe that the proper training is on order. Any move towards the rail should be treated the same way, as any move towards the cake on the master's plate
Some work with dog is necessary, but it is the charm of dog's company, isn't it?
We have three dogs - one of really big breed (140 lb) and two of miniature breed (4-5 lb each). We do not have a netting (big one would be able to jump over at any moment, small would be able to sneak through any opening You will leave for operating the anchor
or warps) but we spent enough time on training with them to feel they are rather safe on board.
All the best