Caution: Translations of Quran and Ḥadīth may lead to possible misapplications and misinterpretations. This site is intended for students of sacred knowledge that are proficient in comprehending classical Arabic and have a strong foundation in Islamic sciences. Also note that religious injunctions rely on several aspects beyond what one may glean through reading individual aḥādīth.
bayhaqi:404Abū ʿAbdullāh al-Ḥāfiẓ And ʾAbū Muḥammad b. Yūsuf > Abū Bakr b. Isḥāq > Muḥammad b. Ghālib > Abū al-Walīd > Shuʿbah > Ashʿath b. Sulaym Fadhakarah Biʾisnādih

[Machine] The Prophet ﷺ used to prefer to do everything on his right side to the best of his ability, including walking, wearing shoes, and performing ablution.  

البيهقي:٤٠٤وَأَخْبَرَنَا أَبُو عَبْدِ اللهِ الْحَافِظُ وَأَبُو مُحَمَّدِ بْنُ يُوسُفَ قَالَا نا أَبُو بَكْرِ بْنُ إِسْحَاقَ نا مُحَمَّدُ بْنُ غَالِبٍ نا أَبُو الْوَلِيدِ نا شُعْبَةُ عَنْ أَشْعَثَ بْنِ سُلَيْمٍ فَذَكَرَهُ بِإِسْنَادِهِ

أَنَّ النَّبِيَّ ﷺ كَانَ يُعْجِبُهُ التَّيَمُّنُ مَا اسْتَطَاعَ فِي شَأْنِهِ كُلِّهِ فِي تَرَجُّلِهِ وَتَنَعُّلِهِ وَوُضُوئِهِ  

رَوَاهُ الْبُخَارِيُّ فِي الصَّحِيحِ عَنْ أَبِي الْوَلِيدِ وَرَوَاهُ مُسْلِمٌ عَنْ يَحْيَى بْنِ يَحْيَى

See similar narrations below:

Collected by Bukhārī
bukhari:426Sulaymān b. Ḥarb > Shuʿbah > al-Ashʿath b. Sulaym from his father > Masrūq > ʿĀʾishah

The Prophet ﷺ used to start every thing from the right (for good things) whenever it was possible in all his affairs; for example: in washing, combing or wearing shoes.  

البخاري:٤٢٦حَدَّثَنَا سُلَيْمَانُ بْنُ حَرْبٍ قَالَ حَدَّثَنَا شُعْبَةُ عَنِ الأَشْعَثِ بْنِ سُلَيْمٍ عَنْ أَبِيهِ عَنْ مَسْرُوقٍ عَنْ عَائِشَةَ قَالَتْ

كَانَ النَّبِيُّ ﷺ يُحِبُّ التَّيَمُّنَ مَا اسْتَطَاعَ فِي شَأْنِهِ كُلِّهِ فِي طُهُورِهِ وَتَرَجُّلِهِ وَتَنَعُّلِهِ