Personally I really like Lightroom. As well containing one of the best RAW converters out there it's also really good at managing your images, and producing excellent final output, be that printing directly, or via a file to a lab, posting to various websites such as Flickr, Photobucket or even Facebook. It will also produce slide shows and web galleries for you. The big advantage with LR is that for probably somewhere over 90% of images the LR RAW processing engine is all that you will actually need. The local brush edits now allow you to do basic cloning work (much improved in LR5) so much reducing the need to move an image to a pixel editor at all. It is now really only for complex cloning and combining images using layers that most photographers will need to fire up a pixel editor.
You talk about working on JPEG images after they have been converted from the RAW. Very often if you use LR you will never actually need to produce a JPEG file that you will keep locally. LR will upload your images directly to most of the major web hosts without generating an intermediate JPEG file. JPEG files become something you generate for a particular use and then delete, which is great as you always use the latest edits if you happen to make any changes.
In order for LR to do it's magic though it has one need, it uses a database file to keep track of all of your images, and the changes/edits you make to your files. So although you can keep the files absolutely anywhere on your computer's file system you must tell LR where they are. It is also a good idea to only move the files about from within LR, so that it is able to keep track of the changes. You can move files outside of LR, but then you have to tell the program where you have moved them to yourself. It's not too hard to tell LR where the images have gone (as long as you remember where you put them), and you can do whole folders, or even folder trees at once.
Alan