This excerpt is taken from Sheikh Abu Hamza Abdul Khaliq Siddiqi's book Sahi Fazail-e-Amaal.
عن أبى هريرة رضى الله عنه قال: قال رسول الله صلى الله عليه وسلم : إذا انتهى أحدكم إلى المجلس فليسلم ، فإذا أراد أن يقوم فليسلم ، فليست الأولى بأحق من الآخرة
It is narrated from Sayyiduna Abu Hurairah (may Allah be pleased with him) that the Messenger of Allah (peace and blessings be upon him) said: "When any one of you enters a gathering, let him say Salaam, and when he rises to leave, let him also say Salaam, for the first Salaam is not superior to the second."
Reference: Sunan Abi Dawood, Book of Manners, Chapter on Salaam when leaving the gathering, No: 5205 - Sunan Tirmidhi, Chapters on Seeking Permission, Chapter on what has been narrated about greeting when standing and sitting, No: 2706 - Al-Silsilah Al-Saheehah, No: 183.
Sayyiduna Abu Umamah (may Allah be pleased with him) says that the Messenger of Allah (peace and blessings be upon him) said:
إن أولى الناس بالله من بدأهم بالسلام
"Indeed, the person closest to Allah among the people is the one who initiates Salaam."
Reference: Sunan Abu Dawood, Book of Manners, No: 5197 - Sunan Tirmidhi, No: 2694 -
Al-Albani (may Allah have mercy on him) declared it "Sahih."Sayyiduna Bara bin Azib رضي الله عنه narrates that the Messenger of Allah صلی اللہ علیہ وآلہ وسلم said:
When two Muslims meet and shake hands, Allah forgives both of them before they separate.
Reference: Sunan Tirmidhi, Kitab al-Isti'dhan, Bab Ma Ja'a fi al-Musafaha, No: 2727 -
Al-Albani رحمه الله has declared it "Sahih".