There is no requirement to open the files in one program or another. Just get the files transferred from the memory card to your PC. But you need to be aware of what your options are once the files are on your PC's hard drive.
For Nikon RAW files (.NEF), Nikon sells Capture NX 2, which is their proprietary RAW converter. From Capture NX 2, you can save a RAW file into other standard files, such as JPEGs or TIFFs. In addition, you can save changes made to the RAW file and keep it as a RAW file so that you can open it again in the future and make non-destructive changes to it again. This is the equivalent to a digital "film negative" - you can just simply open the RAW file, make changes, or back them out, and you won't degrade the image quality or conversion potential of the file as long as you stay in RAW format. Then you can generate JPEGs that are then fit for purpose from the modified RAW (web, print etc).
PSE 8 can also open the Nikon RAW files (using the correct Adobe Camera RAW plug-in which is free for download), but you must save the changes into another format, such as JPEG, TIFF, or proprietary Adobe formats like PSD or DNG). You already have PSE8, so you don't need to spend the additional money on Capture NX 2. Your flexibility in non-destructive edits is more limited. You can use a format like PSD or DNG that lets you back out changes as needed, but now you need to keep two files - the original RAW in case the PSD or DNG is too far gone to recover, and a matching PSD or DNG that has all your preferred changes to date. From there, you can generate JPEGs that are fit for purpose (web, print, etc).
For the JPEG files that came with the RAW file, you can generally use any photo-editing program that will recognize the format. This includes PSE8 and Capture NX 2. The in-camera settings (including sharpness, quality, size, noise reduction, color space, white balance) are all hard-coded into the photo. You just lost all flexibility in being able to change any of those settings. The accompanying JPEG is more useful for things such as immediate posting to the web (this assumes you got all the in-camera settings correct to your satisfaction, and the size/quality of the image is small enough to suit the less demanding requirements of internet photos). Or use them as electronic proofs - which speeds your culling of the photos - not all photos are keepers and you can use the JPEG to quickly tell which ones are out of focus, improperly lit, not correctly framed, etc - in essence, which ones are the keepers and which ones get deleted without having to open the RAW file.