Basswood
The default wood for almost every project in the library. Soft, fine, even grain with very little tendency to chip or tear out, which is exactly why it's the standard beginner wood — it forgives inconsistent blade angle and pressure while you're still building control. Sold pre-cut into small blocks (1x1x2in up to 1x1x4in and similar) by most whittling suppliers, which is also why the library's block sizes cluster around those dimensions.
Spoon blanks (species varies)
The two spoon projects in the library call for a "spoon blank" rather than a specific species — a rough-cut, roughly spoon-shaped piece, often a harder or more figured wood than basswood (cherry, maple, birch are common) since a finished spoon needs to hold up to actual use. Requires a hook knife in addition to a straight knife, see the gear guide.
Flat boards / general stock
A couple of projects (the letter opener, the chess board) use flat stock rather than a small cube — a longer basswood plank for the letter opener, and any flat board for the chess board. Worth keeping some flat scrap on hand separately from the 1x1 blocks.