Culling the photos is an important skill that all photographers need to develop.
If you are shooting lots of images using a high frame rate, you naturally have lots of images that you neither want nor need. One or two of the burst are worth keeping, the rest are junk.
I shoot lots of sports, running about 1200-2000 per day for an all day event.
During the initial culling:
5% are immediately deleted due to technical problems that cannot be fixed in post processing, usually out of focus.
50% are judged to have artistic problems and will eventually be deleted, "grade B".
The remaining 45% "grade A" are judged good enough to be sorted and potentially processed.
Any sorting and organizing at the file level happens here for the grade A photos.
The grade A images are imported into Lightroom.
A second round of triage picks the photos that will be publicly available for viewing (3+stars, 30-50% of the grade A).
These 3+ photos are processed and exported, the JPG files are uploaded to my website and to the event organizers as needed.
The grade B photos are deleted from the hard drive.
The grade A photos and their exports are backed up to external drives and to DVD, and eventually removed from the original hard drive.
My personal photos do through the same process, but the grade A photos will remain on the hard drive.
Your grade B photos will never get processed and will never be shown to anyone, thus there is no sense keeping them. If a few of them have sentimental value, bump them into the grade A category, then release the disk space to something useful.
Your files need to be backed up onto multiple drives. This covers the most common problem, drive failure, which I have had happen.
Off-site storage is a good idea as it guards against things like house fires. I don't bother as this is a risk I am willing to take. My website can serve this purpose for many of my images.