I have a safe in my apartment and one back in my parents house. I also have a safe deposit box. As someone who has been the victim of an *attempted* burglary ("home invasion") and has seen plenty of people's apartment robbed, I think owning one is definitely worth it.
My apartment safe I holds my jewelry, computer backups, safe deposit box key, passport, emergency cash, and any important documents I either readily need or don't have time to put back in the safety deposit box. If I'm out of town for a while, I might put some other valuables in there too. At my parent's home, I have a small gun safe. For very important items and valuables (stock & bond certificates, legal documents, insurance policies, social security card, birth certificate, etc), I have a safe deposit box which costs ~$20/month.
Considering your needs include fire and theft protection for temperature sensitive items (hard drives). Generally, the fire resistance time isn't a huge concern as fires spread/move. You might also want to ensure that your safe is adequately waterproof (in case of floods or extinguishing fires).
I'm not a fan of the digital keypad locks many consumer safes feature. I've worked in places that bought these for additional storage and often the electronic function broke pretty quickly for whatever reason (Sentry and First Alert, in my experience). I'm a pharmacist and having worked in pharmacies in the past, a quality safe is nice to have when you're in and out of the thing 20x+ a day. In the case of getting in and out constantly, electronic is far more convenient, but these are very expensive safes (thousands of dollars). I wouldn't pay extra money for the keypad. Avoid First Alert, their quality overall seems pretty bad in my experience.
I use something much like this. It's nothing too special, but enough to keep things relatively safe in the event of theft or fire:
http://www.amazon.com/SentrySafe-SF...sbs_200_1?ie=UTF8&refRID=1AP65A1BKG3Q4Z4QTR4P