I saw your post and I thought I would reply if no one has been able to help you yet. Do you have an audio interface to record your band with?
I am not sure what the processing power of the mac mini is or what all the Logic Express version does but if you have an audio interface you can get started but keep in mind that drums can eat up a lot of inputs. I have a total of 8 inputs. Each input can go to a track so the band plays together and each instrument records on it's on track.
If you don't know anything at all about the software keep in mind in order to record you have to select the track and click the record button on the track and click record on the transport if you have something plugged in to the audio for a audio track.
I hope this helps,