I am developing small ArcGIS Visual C# applications.
I can display maps on the interface.
Which map format (.jpg , .tif , .png / ArcGIS supported other map formats ) provides the best performance?
Here are some questions you should ask yourself if you want a good answer. If you are serious about performance you'll want to think of answers to most if not all of these questions!
If you just want a quick suggestion for typical georeferenced true color aerial imagery that resides locally or on the network and is divided into manageable sized tiles (think USGS quarter-quad), and is meant to be displayed on a typical, current desktop PC, use 8-bit, 3-band JPEG-compressed GeoTIFFs at 75% quality. This should provide a good mix of performance, space efficiency, and display quality.