2mm is definitely more robust. Are you looking at doing straight lines only, or curved edges? 2mm will struggle on tight inside and outside curves due to the memory effect of the banding, it will want to spring back to straight before the glue sets. By tight I mean sub 50mm radius. The machine recommended radius is 50mm, but you can get down to a 20mm internal radius edge done with thinner banding and the right speed and technique.
Round edge or straight comes down to personal preference. Either way, you typically use banding wider than the edge of the panel and trim to size afterward. This can be done with the MFK trimmer using a straight bit or a curved bit that will give you the straight or rounded edge that way.
Going back to the 0.8 vs 2mm debate, I use 1mm (close enough to your 0.8) for panels that need to 'look' right and the 2mm for panels that are likely to get knocked (eg inside a pantry).
