Choosing an ayanamsa: what to consider
Choosing an ayanamsa is a decision about the reference point of the zodiac. This site offers Lahiri, Raman and KP, and the choice changes every planet's sidereal longitude by the difference between the values.
What it is
Lahiri is the most common in Indian almanacs and is the site's default. Raman is used by some practitioners and some books. KP is used in the Krishnamurti Paddhati. Each has its own base value at J2000.
How it is worked out or read
Consider your teacher, book or almanac first, because they use one ayanamsa and comparisons work best with the same choice. If you have no preference, use the default, and compare with a second ayanamsa if a planet lies near a sign boundary.
Where it appears on this site
The ayanamsa is a choice in each tool. The articles Lahiri, Raman and KP describe each.
What the choice changes
The ayanamsa is the angle subtracted from tropical positions to obtain sidereal ones. At present the Lahiri ayanamsa is a little over 24 degrees. Changing the ayanamsa moves every planet and the Lagna by the same amount, so it never changes the angles between planets, their aspects, or the tithi. What it can change is any classification that depends on a boundary: a planet's sign, its nakshatra and pada, its navamsha, and the Moon's nakshatra that starts the dasha sequence.
The options on this site
This site offers three. Lahiri, also called Chitrapaksha, is the ayanamsa recommended by the Calendar Reform Committee and used by the national almanac and most Indian almanacs and software; it is the default here. Raman, associated with B. V. Raman, is smaller by roughly one and a half degrees, and is followed by many who learned from his books. Krishnamurti, used in the KP system, differs from Lahiri by only a few minutes of arc, and is the natural choice for anyone working in KP.
How to choose
For most readers, the best choice is the one used by their tradition, family almanac or teacher, so that their charts and calendar agree with the sources they use. If you have no tradition to follow, Lahiri is the most widely used and the easiest to compare with other sources. If you are learning from a particular book or school, use its ayanamsa while you study it. What matters most is consistency: use one ayanamsa for all the charts you compare.
When it makes a difference
For most charts, switching between Lahiri and KP changes nothing visible. Switching between Lahiri and Raman changes something in a minority of charts: a planet near the start of a sign may move back into the previous sign, or the Moon may move into the previous nakshatra, changing the dasha sequence. If a chart has planets or the Lagna within about one and a half degrees of a boundary, it is worth looking at it under both and noting which features depend on the choice.
No single correct answer
There is no astronomical fact that settles which ayanamsa is right, because each defines the starting point of the sidereal zodiac by a different convention. The differences are matters of tradition and definition. A reader who understands this can move between sources without confusion, and can explain a difference in a sentence rather than doubting either source.