Your original picture looks to me like the rounding comes all the way to the bottom of the board. If that is what you want, you need a 3/4" radius for a 3/4 inch board. Since you will be cutting the entire edge of the board, there is no place for the guide bearing to follow... the router would normally be mounted in a router table so you could use the router table fence.
In practice, almost all of the roundover work I do is with a 1/4 inch radius on a 3/4 inch board. In that case, there is plenty of edge left to guide the bearing and keep the cut straight.
If you are just starting, I suggest that you get a 1/4 inch radius roundover bit, and practice with that. For example, going around the corner (cut the end grain first, round the corners before rounding the top, etc.). If you really want a 3/4 inch radius like the picture, and don't have a router table, clamp another board under your work piece for the guide bearing to follow, but don't try that as your first cut.