The Marian Antiphon for most of the year - from Trinity Sunday through to just before the 1st Sunday of Advent.
In English this is known as Hail Holy Queen.
Some say the Solemn Tone is for feast days and Sundays. I've also heard the Solemn Tone is the proper one and the Simple Tone is a concession for those who need to take it easy. Go with what your superior says and if you're not under a superior, then it's your call which one you sing.
More information: littleoffice.brandt.id.au
Salve Regina - solemn tone