“Back saws” are specifically designed for fine joinery work (they have a rigid steel or brass back to keep the blade stiff). Dovetail back saws are the smallest back saws (typically 8-10″) and are configured with fine rip-filed teeth (15-20 ppi) for cutting along the grain (think dovetails). Thinner blades (0.02″ ish) are preferred and I like the pistol grip handle because of my big hands (see above).
While many woods can be used for carving, there are some clear favorites, including Aspen, Basswood, Butternut, Black Walnut, and Oak. Because it has almost no grain and is notably soft, Basswood is particularly popular with beginner carvers. It is used in many lower-cost instruments like guitars and electric basses. Aspen is similarly soft, although slightly harder, and readily available and inexpensive. Butternut has a deeper hue than Basswood and Aspen and has a nice grain that is easy to carve, and thus friendly for beginners. It's also suitable for furniture. While more expensive that Basswood, Aspen, and Butternut, Black Walnut is a popular choice for its rich color and grain. Lastly, Oak is a strong, sturdy, and versatile wood for carving with a defined grain. It's also a popular wood for furniture making.