Hi, yes, I imagine trying to digest a lot of technical information quickly can lead to headaches
To give more useful answers, it would be best for you to provide some more details of your current equipment & software.
A few general suggestions to your questions:
1) Media, don't bother saving a few $, even so called premium media is stupidly cheap these days (apart from archival/specialist grade media). Taiyo Yuden/Verbatim are the 2 most easily available safe choices. I prefer +R media as every writer I have used seems to work better with them.
Standalone compatibility should not be an issue with any modern standalone drive, I have used +R media (no bit-setting, though you may need to for some standalones) on many drives with no problem, even a very early generation standalone.
2) Using ICE ECC or PAR2 or some other program which can create recovery data can provide an extra layer of error protection to your data. Idealy, depending on your paranoia/financial ability/space, multiple copies of your data, stored on different media (CD/DVD/HDD/Flash/Tape/etc) at multiple locations with regular testing should provide near 100% confidence in it's survival.
Or if your not quite that worried, 2 copies of your data stored on 2 different brands of DVD media which is checked on a regular schedule should give you a high enough probability of data safety