In order to get the images organized and help me find out a particular photo with ease in the future, I have started to rename awkward files (such as IMG_0001) into meaningful names (such as 2015-12-21 event_location), add relevant keywords, write detailed titles and captions, rate photos by stars, etc. With only several hundred photos processed, I understand that this is absolutely a boring task and it takes a lot of time, so I'm wondering if this is really an essential step into effective digital photo management?
I would skip the renaming. The keywords and titles and captions ought to be sufficient for you to find the photos in Lightroom.
Furthermore, inn order to for the titles, captions, and keywords that I have added to be understood by other programs, I must save the metadata to the original files themselves, right? While I understand that Lightroom only writes metadata to the non-image header of the files and thus does not damage the originals, the fact that the date modified fields being changed into a recent date really made me feel uncomfortable. This is especially true for the photos that were taken a couple of years ago.
I do save the metadata to the files, just in case there is a future need for other programs to access this information, and also in case I can't launch Lightroom (wHich has never happened to me), then I can find the photos using my operating system's search feature. The capture date is not modified, and so you should be able to always search for the photos by capture date within Lightroom, and outside Lightroom as well.
So, what do you think would be a better choice: should I save the metadata into the files and do not have to worry about software compatibility, as each photo has its own metadata within, or should I rely only on Lightroom and save all settings into a single catalog file? (I work mainly with JPGs so metadata is saved directly into the original, not in any XMP sidecar files)
I do both. I don't find the changed "date modified" field to be an issue. As I said, Lightroom allows you to search by capture date, and your operating system probably does as well.