Depends what you are saving it for. If you are saving to publish on the web, yes JPG is the way to go (there is also a handy "save for web" option in the file menu, although it will strip out all your EXIF data).
If you want to save all your processing edits so you can go back and tinker with it later, save as PSP as this will retain all the layers, but it will likely be quite a large file size.
If you want to save it as a "master" or archive copy, then save as PSP again, and "flatten layers" beforehand to reduce file size or save in another lossless format (such as TIFF).
If you have shot in RAW, keep that as your unedited master.
I will usually keep the RAW. If I have edited in PS, I'll have a PSP version (usually "flattened" to keep file size down), then just save to JPG by opening the PSP file as and when I need to upload to web or send someone a Hi-Res version etc.
Don't keep a single copy of a JPG file and keep saving it as JPG. JPG is not a loss-less format, and data will get discarded each time you save it (i.e. every time you make copies of copies, the image will reduce in quality, similar to the effects seen when everyone used to copy VHS tapes back in the day...)
HTHs
