What are the recommended screwdriver types for furniture repair and construction?

Most types which would be appropriate for this purpose are familiar names. Phillips, Flat Head, Cabinet, Robertson, Star, Hex, Clutch Head and Nut Driver, for example. Get an interchangeable bit set and one screwdriver can take care of most of those types. These can be found on the Yankee Screwdriver and the Ratcheting Screwdriver. Other commonly used screwdrivers for this purpose would be the Offset and the Tack Claw. However, which type you require will depend entirely on what you are building.