As noted by others, it is difficult to come up with a hard and fast rule for remote sensing analyses. There are many different factors to consider based on what your end goal is, the type of environment (desert vs jungle vs urban), complicating factors (clouds or terrain or shadow effects), and if you are conducting a temporal analysis.
In the past I looked for comprehensive, general tutorials, and never found one. What I did find is that you generally have to piece together various best practices and fit them to your use case. One option is to search for a scientific paper that has addressed a similar point, and read through their methods. They likely will not list the exact tools they used, but you may be able to reverse engineer similar methods using your software of choice.
All that being said, to try and briefly address the variables in the ArcGIS tool you list:
- Bands: As noted by others, this depends on many factors. Choose bands or indices that will help identify your topic of interest, e.g. urban areas, vegetation health, land/water. See USGS and Landsat 8 band combinations.
- Number of classes: Again, this depends on your project specifics. If you want a water/land mask, you only need two classes (although in practice, I might choose ~3-4, then run the tool again to aggregate areas, e.g. shadows that could be incorrectly identified as water). The quick and fast rule is: Pick the fewest classes that you need. Generally the fewer the classes, the more accurate. For example, having forest/non-forest will almost certainly be more accurate than attempting to classify evergreen, deciduous, mangrove, barren land, etc.
- Number of Iterations: Try the default for now. Fewer iterations will run faster.
- Minimum Class Size:: Again, this depends on your use case. In essence, you are saying what the minimum area for a class needs to be. This will depend on the area of analysis, land cover/use types, and how generalized you want the final classification to be.
- Sample Interval: Once again, this can vary. Leave it as the default and see how the comes out. ESRI has more information on this, and classification in general here.
Sorry to not be of more assistance. Again, it may be frustrating to hear, but remote sensing is very dependent on project specifics. It looks like you have access to ArcGIS, so I would say give that a try and see how it comes out.
If you have time, you may be interested in other programs that I would argue are better suited to the task. One fairly user-friendly option is provided as as a QGIS plugin and the author put together a tutorial. Other options include Opticks and GRASS (both free) and ENVI and eCognition (both commercial). If you are familiar with ArcGIS that will be the most straightforward for now. However, if you plan to keep doing or need more advanced analysis capabilities I highly recommend exploring other options, as ArcGIS is not really intended as a fully-featured image-analysis program.