If all you have is a DVD player, you shouldn’t be burning Blu-ray discs. Blu-ray uses a different type of laser, which is a different frequency and color from the red laser used for DVD’s. So, a regular DVD player, or DVD drive in a computer will not be able to read a Blu-ray disc at all.
If you want to store data on a Blu-ray disc, and use a Blu-ray burner in your computer, that combination will work for you. Simply burning video onto a Blu-ray disc will not change it automatically to Blu-ray video format. If the video is DVD-video format now (Video_TS folder and Audio_TS folder), it might not play on anything except a computer drive, as most stand alone Blu-ray players might not recognize DVD-video on a Blu-ray disc.
Long term storage on any one medium is not advised. You should keep copies of important data using various storage strategies, including hard drives, optical discs, online storage, etc. Blu-ray discs are not immune to failure, so it is best to buy high quality media, like Verbatim (not their LTH discs), FTI/Falcon, or Panasonic.
The best way to store optical discs is in individual cases. These can be the slim cases or the regular size. I personally use slim cases in a custom made cabinet, and store them on the edge of the case, not flat. Storing discs in a cakebox is not optimal, but is much better than the soft, cd wallet style.