RAW files are significantly better than JPEGs as you have all the information coming off the sensor. What happens in camera is that the electronics takes this raw information and guesses how best to convert it into a JPEG, (colour balance, sharpness, etc). In the process a lot of information is thrown away, particularly in the light and dark parts of the picture. Now for us the information in the blacks is particularly important and so much detail can brought back into a final image when using the RAW sensor data. However you need the right software to do this. I'm not sure how well Paintshop Pro does RAW conversions, but I guess it'll depend on what version you have. There's loads of software out there that does a great job. I use Adobe Lightroom, which is something like £20 a month, (with PhotoShop).
It's a slippery slope though… Instead of just copying photos to your computer and enjoying them you'll then end up spending hours fiddling with the photos. Mind you, that's the advantage of shooting both RAW and JPEG. You've got your quick prints, (JPEGS), but you've also got the negatives, (RAW), if you want to make a really nice print.