...decent shots along the fence line of a motorcycle race...
This part is going to be tough with this:
...I was thinking of maybe looking in the $300 range. Anything decent there?
These are in the range, sorta'.
Panasonic LX-5
Olympus XZ-1
Canon G12
Canon S100
Nikon P7000 - not in the same league as the others, but lower priced
You're not going to find a new DSLR for that kind of money and getting results from a point-and-shoot with moving subjects is also difficult, but it can be done as long as you have a point-and-shoot with manual focus.
Example: set aperture to f/4 - 5.6, keep shutter speed high by adjusting ISO, prefocus (using manual focus) at about 10 feet (hyperfocal distance) and then shoot all day - everything will be in focus with a small sensor camera like those listed. You'll just have to get your timing down due to the shutter lag that point-and-shoot cameras tend to have but this will at least get rid of the worst part of the P&S cameras - lag due to slow focus.
PM me if you need more specific answers.