I'm not familiar with the file formats that ArcMap supports, but assuming it can read both MBTiles and png images with KML calibration files (Google Earth ground overlays), then you could use either.
If MBTiles is supported, then it is likely the better choice for large mosaics - e.g. where the pixel size is going to exceed a few thousand in either dimension - as there is a limit to the size of individual png files that can be exported. Having said that, you can select the "tile" option when exporting in the png format, and this will split an image into a series of 1k x 1k images - it's just not as neat a solution as the single file MBTiles export, which effectively does the same thing but stores all of the images within a database.
If ArcMap supports KML "superoverlays" (doubtful, but possible) then that would be another option. This is another tiled format that creates image tiles at various scales and is good for sharing on the web.
As far as navigation distortions for sidescan - we smooth the GPS track but that is all. In a major update to ReefMaster later this year we will also consider logged headings (if available) which can significantly improve the positional accuracy of sidescan imagery (see our Sonar Viewer application, in which this is already implemented).
