For a digital camera, most filters do nothing to improve quality and can even hurt the image quality. Many people still use a UV filter to protect the lens. It depends on if you think the lower image quality is worth it to protect the lens. For a p&s camera, you might not even notice a difference. I never saw a difference on my S1 with a UV, but the same filter on my DSLR makes an obvious difference. I do suggest the extension tube if you do not mind the exra size b/c it protects the extending lens.
A circular polarizer is a different story. It will degrade the image in the same way, but there are situations where the benefits outweigh the negatives. Do not use it all of the time though. If the light is not polarized, then it does nothing to help.
Also, this is one of those areas where you get what you pay for. Do not go with a low price no name filter.
Kevin