technically you can eat any rabbit it is just that some are better suited for meat because they dress out better (smaller bones, etc.) and convert food to meat more efficiently. I don't really know how well rabbits that would be used for fiber dress out so I can't really answer your question but if you really wanted to dual purpose I would think it would be a possibility with just about any rabbit you chose.
Classically the "fiber" rabbits are the angoras, which you brush and pluck to get hair to spin into yarn.
If by "fiber" you mean skins, you should choose a breed with pelts that appeal to you. The standard Rex is a popular fur rabbit, since it has it's unique velvet like fur. The Satin is also popular because of it's special fur that looks and feels satin-y. Both come in a wide variety of colors, and both dress out to a decent weight. Avoid the mini's of both breeds, since their dress weights are very small.
ALL rabbit fur is soft to the touch, but it's important to keep in mind that the normal harvesting age of a young fryer does NOT produce a quality fur. You would need to allow the rabbit to age until it's full adult coat is in, or even better wait until their winter coat grows in, before harvesting if you goal is a quality pelt for resale. The trade off would be a less tender, but perhaps more flavorful, carcass.
You could eat some of the angoras if you want, but I can't imagine they grow quickly or develop much flesh with so much energy going to theri coats, though they are large enough. Perhaps you could consider getting a few meat-type does (like new zealands or californians), and breeding your angora buck(s) to them.
Actually, the French and Giant Angoras are commercial in type. The Satin Angora is, too, though I think the softer wool of the Satin might be a little harder to spin. I understand that people that are producing Angora wool commercially use neutered bucks as "woolers," because intact bucks tend to mess their own wool up with their spraying (having raised Jersey Woolies for many years, I can confirm that this is usually true, at least to some degree.