Round brilliant: the classic for a reason
The most sparkle of any shape, and the only one with a full cut grade.
The round brilliant has 57 or 58 facets designed to return as much light as possible. It still leads engagement-ring choices in Canada. It's also the easiest shape to shop: GIA and IGI give rounds a full cut grade, so "Excellent" (or "Ideal" at IGI) is a reliable first filter. Rounds cost more per carat than fancy shapes because more of the rough is cut away. They hide inclusions and colour well, though, so you can often go a little lower on clarity and colour without seeing a difference.