What is the best $300 digital COMPACT camera for lense quality, quickness, and control of the shot?

Check out the Fuji FinePix E550 or newer E900 (may be over $300).

I am a nature and outdoor photographer and have used the E550 for several years. It is feature rich with presets for nite, portrait, landscape, sports and 640x480 30 fps movies, and would be good for someone without much experience, as well giving more control with WB, speed, B+W/Color/Fujichrome vivid, macro, on screen immediate histogram, A, P, S, M modes as someone more experienced would use. It is not a "thin" camera. But I don't have a problem taking it anywhere.

Specs are 6.3 MP with 4x Optical, 3x Digital Zoom
Super CCD (one of best imaging devices)
Uses XD Cards (up to 2 GB)
Can take 12 MP Fine or 12 MP normal (excellent interpolation)

One 1 Gig XD card can take about 500 pictures in the highest 12 mp resolution.

The E900 has the same or better features, it is a newer camera model.

I just bought my wife a new cybershot and it is a great camera, that also does short videos. Picture clarity is out of this world.

I've got a canon sd-10 it's a few years old and was $350 when new, but I love it. It's small enough to fit in my pocket and takes great pics and 3 minute clips.

I like my Canon Power Shot. You can get a nice one for around $299.