The answer may be both. You may want to initially start with paper files and move to computer genealogy or, depending on the nature of your primary records, you may wish to preserve certain documents and photographs for future generations.
Personally, I use both. I like having the original documents stored in a file cabinet for comparison sake, but I back up all my records and photographs on computer and back up the computer data again. In essence, I have three sets of records.
That said, computerizing your genealogy brings with it several advantages. It takes the place of massive amounts of paper and reduces the footprint of having to store all that data in bulky, large file cabinets. The computer also provides a space in which to neatly combine your genealogical pedigrees, your photographs, your videos, and your family stories in an organized fashion. And, if you use a laptop, your entire ancestry is available in a nice portable vehicle that you can transport to libraries, genealogical societies, or state archives where documents are not available online.
The computer also opens up the world of internet genealogy. Amateur genealogists and family historians gain access to records previously unavailable to them. Genealogical forums help reconnect families and sort out pedigree problems. Website development creates a new media to display family history and share ancestry among relatives.
So, is computer genealogy for you? Yes, it just makes sense. Computers are much more affordable and you can safely keep your ancestral records on your preferred storage device or post to your own website. With backups of your ancestry, it's a no brainer. Computerized genealogy is the way to go.