I think the best color to use is one that is pretty close to the color of your Labradoodle. :)

Yes, bring a little baggie of shed hair (the undercoat, if he/she has one, or whatever gets shed most) when you look at fabrics. We matched our TV room sofa and area rug to the undercoats on our two aussies, and it makes a big difference. We still clean often, but the sofa and rug don't look doggy. It also sometimes helps to choose a fabric with a subtle texture or pattern--like a small herringbone or other weave in two similar shades. This helps camouflage.

Labradoodles don't shed. I want one but the cat of the house says no way.

So as a pet lover who has no ability to say "no" I vote for ultrasuede (the real deal). I would even reupholster the piece in this (price may be comparable).

We have 2 Aussies as well who are allowed on furniture. We slipcovered sofa in living room with ultra suede and it has been excellent with the dogs. Shows no fur and washes like a dream.