A garden hose is fine. Note that there are drinking water hoses out there for such purposes as this. (Standard garden hoses have been shown to potentially leach harmful chemicals from the plastics they are fabricated from.) Your call on that.
Yes--before you fill it, position your large water barrel where it will sit so you don't have to wrestle with it afterwards. For your water source, use city treated water if possible so you know you don't have contaminated water right from the start.
For water storage purposes you want to use water preserver concentrate
, not bleach or water purification tabs or any other solution that will suffice if you plan on drinking the water right after purification. The difference is that water preserver concentrate is formulated to actively work for to keep the water pure for five years.
The other approaches do nothing other than purify the water at the start. Without water preserver concentrate, you will need to repeat the process of emptying and re-filling your container every six months to be sure your water has not started to go bad in some way.