The Muslims, Christians, and Greek Orthodox (among others) signed a national pact in the 1940s in order to stabilize the region and create modern-day Lebanon. Because of this national pact, the President of Lebanon must always be a Maronite Christian, the Prime Minister must always be Sunni, and the Speaker of the Assembly of Representatives must always be Shi'a.
http://www.country-studies.com/lebanon/the-national-pact.htmlThe Tarif Agreement in 1989 redrew power, with Christians having to split parliament 50-50 with Muslim representatives. Prior to that, Christians enjoyed an unfair advantage considering shortly after the founding of Lebanon, the Muslim population outnumbered Christians and that the Muslims were being under-represented.
The Free Patriotic Movement is a decent group to throw yourself behind as they are centrists and secular, if you are looking for stability in the parliament. They have pledged support for Hezbollah in a public statement once Hezbollah disarmed. They are reformists which are sorely needed in the area.
The distinction between left and right political parties in Lebanon is very difficult. Hezbollah is militant and right-wing in matters of war, but their economic policies are socialist. They win popular support through their bankrolling of social services.
The SSNP (Syrian Social Nationalist Party) were founded on the principle that all of Israel, Palestine, Syria, Lebanon, and parts of Turkey need to create a super-state called Greater Syria. Needless to say, they are not above using violence to achieve this aim. They are an odd combination of secular and nationalist.
The Progressive Socialist Party runs on the Social Democrat platform, with emphasis on national unity, but in the past they have resorted to violence and recently provoked Hezbollah into armed confrontation with them. I think they have gotten away from their progressive roots.