Overall, your choice of wood and lamination streategy depends on a few variabilities including weight constraints, beam of boat, budget and whether a clear beatiful look is desired. If budget or weight are your primary concerns, I would go for pine. If less work is desired or you want a rich clear finish, I would go for something like mahogany.
The narrower the beam of the boat, the greater the unsupported span of the rigger, so greater reinforcing is of benefit. So our Cambridge Racer (a narrow scull) for example would benefit with extra reinforcing in the rigger (two layers of 6 oz glass over pine,). Our RowCruiser (beamier), on the other hand, has a relatively short unsupported span off both sides, so flex is less of an issue.
For greatest strength to weight, I would recommend pine or spruce. Both these woods have excellent mechanical properties and good strength for weight (better strenght for weight than most hardwoods). The wood alone isn't enough to provide sufficient stiffness, but it acts as a strong coring for outer reinforcing. To add significantly more strength and stiffness the wood needs to be sheathed in fiberglass and epoxy (or other composites). S glass will provide even better stiffness than e-glass, so is highly recommended. Multiple layers of glass can be used if maximum stiffness is desired. Carbon fiber can also be used (this is the sfiffest material), however it is a bit more difficult to work with than glass.
A strong hardwood may be less work, as you may not need any composite lamination (for an application such as the RowCruiser), however, it will be heavier.
Overall, my personal preference - best bang for your efforts and budget is pine with a composite coating. I've only used regular glass, but undoubtedly S-glass would be a step up. And for the pinnacle in strength, stiffness, and weight, I'd recomend carbon fiber. Having rowed over 30,000 km I've become a big fan of reducing weight wherever possible, and this is the way to create the lightest strongest riggers without getting into advanced vaccuum bagging composite techniques.