The Messenger of Allah ﷺ loved to begin with the right side. He would take with his right hand and give with his right hand, and he loved starting with the right in all his affairs.
أخبرنا محمد بن معمر قال حدثنا أبو عاصم عن محمد بن بشر عن أشعث بن أبي الشعثاء عن الأسود بن يزيد
كان رسول الله ﷺ يحب التيامن يأخذ بيمينه ويعطي بيمينه ويحب التيمن في جميع أموره
No references are available.
Sahih. It is also in Kubra, hadith no. 9321. Mizzi said, "This is a mistake, and what is preserved is the hadith of Ashath bin Abu Shatha, from his father, from Masruq, from Ayesha." See also hadith nos. 112 and 5242.