What are the core Mahayana and Vajrayana Sutras?

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.