What I like for small waves, for a shortboard style surf (I let others speak of the longboard shapes):
- As short as possible. Shorter means slow paddle speed, so you have less mobility to flee the crowd to chase waves peaking outside of the normal lienup, and less leeway to go place yourself perfectly for takeoff. For instance, for fast waves breaking in some depth, you will want to keep board length (e.g 8'+). For slow waves breaking on a well-shaped sand bank or reef, you will want a 6'x" board
- As light as possible
- A round or semi-round nose. Avoid blunt square noses, they push water.
- For weak waves, a full square tail, Simmons-like. The more powerful the waves, the more pulled-in the tail.
In my Gong quiver for Hossegor, you can see, from left to right:
- #1 a board for weak fast waves: 8'4" x 120L, semi rounded nose, wide tail but not extreme. A flat rocker. Similar to the Infinity B-Line and others.
- #3 a board for small fast waves: 7'3" x 105L, pulled in tail
- #4 a board for small slow waves: 6'10" x 125L, wide everywhere

A better shape for the #4 (small, slow) was a rounded nose: a bit faster to paddle:

Here in action: Slow waves, 4s period:
And a Simmons of the same size: (second from left):

In action: I had a tiny peak for me alone, 50 surfers were crowding a better peak just nearby:
But now, Gong has reduced his lineup, and the Mob is currently offering a compromise, an hybrid of all these small wave shapes:
A very good shape for "shortboard"-SUPing in small waves.

I do not have good videos of it, only webcam captures, but it shows why on Hossegor sandbanks, the paddling speed is important to go fetch the shifting peaks: