Inexpensive Sony P&S
P mode. This camera allows no direct control over shutter speed or aperture, except how you might manipulate it to do generally what you want through a "scene" mode or zoom choice. Disappointingly it doesn't have a "sports" scene so I don't know what I'll do yet when I want a high shutter. In my limited experimenting with it it does prefer high shutter speed as you zoom out and pick a high ISO. At 25mm (equiv) going up the ISO scale gets the ND filter in play at about 1/300 to 1/400 while at 250mm it's sticking with an open aperture and going high shutter (of course).
You're right about the lens. It's pretty sharp corner to corner, much better than the lens on the those two Canon P&S which were good in the center but pretty bad towards either side, the left in particular on both.