Equal temperament is what most modern fixed-pitch instruments such as pianos use. The octave is divided up into 12 equal intervals. Our ears are so used to hearing these intervals that they may sound normal to us. But players of fretless instruments can do better.
Just temperament is based on integer ratios of 3/2 (perfect fifth) and 5/4 (major third). It has lower major thirds and lower major sevenths than equal temperament. It is probably the temperament to use if you're interested in harmonic blending with other string instruments.
Pythagorean temperament is based on tuning in perfect fifths only. It has a higher major third and higher major seventh than equal temperament. It is probably what you want to use if you're going for "expressive intonation."
The default setting for Intonia is to use an even-tempered scale. If you use Just or Pythagorean temperament, remember to set the Key and Minor options to the key you're actually playing in.
In Just and Pythagorean temperaments, all of the intervals are calculated relative to the tonic of the selected key. In the key of C, the wolf interval appears between G# and E flat. In the key of D, the wolf will appear between A# and F, etc. The tonic note frequency is adjusted so that the open A string is always exactly 440 Hz, or the A Frequency option on the Scale Tab.
Many other temperaments have been used historically. See, for example, http://pages.globetrotter.net/roule/temper.htm. These other temperaments are probably mostly of interest to people interested in historical performance practice. Recall that these temperaments grew out of a desire to make fixed-pitch instruments such as harpsichords and pianos capable of playing in many keys. They may sound better in some keys than others. But the violin is capable of retempering depending on context, so these historical temperaments may not even be relevant.
It you're playing tonal music, choose either Just or Pythagorean temperament according to your goals, and set Intonia's key appropriately. If you're playing music that goes all the way around the circle of fifths, you can either analyze each segment of music in a separate key, or choose equal temperament.
Many players tend to play their leading tones even sharper than the sevenths of Pythagorean tunings. Therefore, it's best to regard Intonia's analysis not as an indicator of right or wrong, but a guide to what's actually happening.