When starting a more in-depth study of the Dharma from a Mahayana and Vajrayana perspective, what are the core (3 most recommended) Sutras (or texts), and the reasons why they are considered important, to have on your reading list in each of those traditions?
I think your question is much larger than can be answered with just three texts. Mahāyāna is not one thing, it is many Prajñāpāramitā, Madhyamaka, Pure Land, Yogacāra, Chan/Zen, Huayen etc. Similarly Vajrayāna is not one thing either.
For the Mahāyāna a comprehensive guide would have dozens of texts. At a minimum:
- Aṣṭasāhasrikā Prajñāpāramitā Sūtra
- Mulamadhyamikākārikā śastra
- Abhidharmakośabhāsya śāstra
- Yogacārabhumi Sāstra
- Sukhāvativyūha Sūtra (x2)
- Sūtra of Huineng
- Saddharmapuṇḍarikā Sūtra
- Avataṃsaka Sūtra
For Vajrayāna the situation is different. Tantras cannot be read on their own. For Shingon the two main texts are
- Mahāvairocana Sutra (aka Mahāvairocana Abhisaṃbodhi Tantra)
- Vajraśekhara Sutra (aka Sarvatathāgata-tattvasaṃgraha)
A good introduction can be found in Kūkai: Major Works by Yoshito Hakeda. Tibetan Tantra includes many more texts, such as:
- Guhyasamāja Tantra
- Hevajra Tantra
- Kālacakra Tantra
But most teaching is done through commentaries. Many of these texts cannot be understood without a commentary. Some of them require specific initiations.
If I had to pick only three, for a practicing Buddhist (as opposed to a scholar) I would recommend:
- A lam rim (~syllabus) text, e.g. Treasury of Precious Qualities by Jigme Lingpa with commentary by Kangyur Rinpoche.
- The Way of the Bodhisattva by Shantideva.
- A prajnaparamita sutra e.g. Edward Conze's The Large Sutra on Perfect Wisdom: With the Divisions of the Abhisamayalankara.