Vertical pianos with free-standing legs not reinforced by toe blocks are generally known as Decorator style. Common decorator styles are Queen Anne and French Provincial, generally in cherry (or Country French in oak), all with curved legs; Italian Provincial, typically in walnut with square legs; Mediterranean, usually in oak with hexagonal legs; and Traditional, most often in mahogany or walnut, with round or hexagonal legs. Matching music racks and cabinet decoration are common furniture embellishments. Furniture-style preference is an entirely personal matter. A practical consideration, however, is that front legs not supported by toe blocks have a tendency to break if the piano is moved frequently.
Grand pianos come in far fewer styles than verticals. As you shop, it is likely you will see only a few different styles, in a number of woods and finishes.
The traditional grand piano case is likely familiar to everyone. It has rather straight or slightly tapered legs, often flaring slightly just above the floor (called a spade leg), and usually a rather plain, solid music rack.
Victorian style (sometimes called Classic style) is an imitation of a style in fashion in the late 1800s, with large, round, fluted legs and a fancy, carved music desk. Variations of the Victorian style have "ice-cream cone" or other types of round-ish legs.