The problem with using the bookshelf speakers, that unless they are near the tv, when you are watching tv, the sound is going to be off, and actually make it sound worst. You can still go with both options, and it would not be high end, but they would probably appreciate the sound quality better.
As for going back to your original question, and moving up to 5.1, you are going to find that speakers sound differently to everyone, and getting decent bookshelves for under a $100.00 can be done, but I would have the parents make the final decision, than getting something that they do not like.
As for the current equipment and using a soundbar for the output, you would use a rca to rca from the Tape out to the sound bar input, and they would be able to use the sound bar for listening to the fm radio or turntable. But keep in mind, that you parents are going to have the last say, and what ever you like, you always know that they will not like, or just don't care in the end.