As mentioned, a softbox is just something that goes over your light. First you need to decide on the light you want to use.
You could get a continuous light type (regular light bulb etc.) or you could get a flash/strobe (either a 'hot shoe' type flash or a studio style 'strobe'.
If you are shooting people, I'd recommend the flash/strobe.
A flash unit is a lot more portable, since it can run on AA batteries. And with a wireless flash trigger, you could be wire free.
A studio type light will probably be more powerful and will likely recycle faster, but it will need to be plugged in. You could use a portable battery pack, but those get to be big & heavy, not to mention that the light itself it bigger & heavier than a flash unit.