Xenyx, your firebox is your new sound card. YOu will not be using the computers sound-card anymore.
As for hooking up to an external mixer, there are a few ways, depending on the goal. The general reasons people use an external mixer with an interface is for additional inputs/outputs and routing capabilities, or for using the mic pres on the board in conjunction with the mic pres on the interface. Also you may want analog EQ in the recording chain or an external compressor or effect inserted in the channel during recording or playback. I have used this type of setup for a long time, even with higher end interfaces such as my RME. I currently use a Mackie ONYX as my interface/mixer and I appreciate the options it provides me.
If those idea makes sense to you or interest you then an external mixer is a good idea to use with your firebox (your new sound-card).
My feeling is that you can start with just your firebox and get a feel for what you need.
Good luck,
Much respect and blessings