I would be happy to help you. Keep in mind the Mac Mini is not recommended for running presentations on MediaShout as they typically do not have dedicated video cards (one of the minimum requirements). With the right optimization they may do okay for some functions, but just wanted to make sure that was noted if it hasn't been already.
For the question regarding the monitor, that would have no affect on MediaShout. There's not really anything we could advise specifically on what to pick as it would be up to your personal preferences for size, etc. We used to have to specify to make sure it was at least able to display 1280x768 but honestly just about ANY monitor you get these days that came out in the last 3-4 years at least should be able to display that and much higher.