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Theravāda works from the Pali canon and preserves the earliest form of Buddhism more completely than anything else running today. The global mindfulness movement, ten-day vipassanā courses and the four foundations of mindfulness all trace back here.
One thing first: "Hīnayāna" is a name given by Mahāyāna polemic and never used of themselves, and today's Theravāda is not the same thing as the schools that were being criticised. The proper name is Theravāda.
It works from the Pali canon, organised around the four noble truths, the three marks and the twelve links of dependent origination. The doctrinal framework is far simpler than that of the Mahāyāna schools, and the precision it asks for in practice is higher.
The aim is to exhaust the defilements and reach arahantship. Becoming a buddha, a fully self-awakened one, is a road a very small number of people vow to walk over an extremely long time. It is not the general goal. This is the fundamental divergence from the Mahāyāna position that all beings will become buddhas.
The Buddha is a teacher rather than a saviour. There is no notion here of being received by another power. You walk the road to the end yourself.
Dīgha, Majjhima, Saṃyutta, Aṅguttara and Khuddaka. The Majjhima Nikāya (MN) is the best way in: moderate length, tightly focused.
Fifth century, the encyclopaedia of Theravāda practice. The forty meditation subjects and the sixteen insight knowledges are all in there. Large, and extremely clear in structure. The most systematic practice text listed anywhere on this site.
The Abhidhamma in condensed form. If you want to follow the Theravāda analysis of mind, start here.
Collected talks by modern teachers such as Mahasi, Pandita and Ajahn Chah. Widely available in translation and easier to get into than the classical literature.
Mindfulness of breathing, loving-kindness, contemplation of the unattractive, the ten kasiṇas and thirty-six more. The Visuddhimagga describes every one of them in detail. It is the most complete catalogue of meditation methods in Buddhist history.
Body, feeling, mind and dhammas as the four foundations; the insight knowledges run in sixteen stages from the discernment of mind and matter through conformity knowledge, path knowledge and fruition knowledge. No tradition maps progress in finer grain.
The "new Burmese method" of Mahasi Sayadaw (1904–1982): no prior jhāna training, the rise and fall of the abdomen as the main object, silent noting throughout ("rising", "falling", "thinking", "pain"), sitting and walking strictly alternated. The Pandita and Chanmyay lines branch off it. The Sunlun tradition, founded by Sunlun Sayadaw (1878–1952), is a separate Burmese line with a different technique.
U Ba Khin (1899–1971) → Goenka (1924–2013). A standardised ten-day course: three days of ānāpāna to build concentration, then systematic sweeping of the body observing sensation, using awareness plus equanimity to cut habitual reaction. No fees, donations from old students only, 200+ centres worldwide.
Ajahn Chah (1918–1992), following Ajahn Mun. No short intensive courses and no maps of insight knowledges. The work is monastery labour, contact with the teacher, strict observance of the precepts and ascetic practice. Western branches include Amaravati in England and Abhayagiri in the United States.
First: "Hīnayāna". The word comes out of Mahāyāna polemic. Today's Theravāda is a different thing from the Sarvāstivāda and the other schools that were being criticised.
Second: meditation was never a mass activity in older Theravāda. Intensive insight meditation is a modern Burmese revival, from the late nineteenth century into the twentieth. Traditionally meditation was mostly the province of a minority of forest monks, while most monastics worked at keeping the precepts, chanting and teaching. The popular equation of "Southern Buddhism" with "meditation" describes a movement a little over a century old.
Third: it is not a simplified Buddhism. The Abhidhamma analyses mind at a precision comparable to Yogācāra, and the practical detail in the Visuddhimagga goes well beyond most East Asian literature.
If you want to actually start practising, the Theravāda resources are the most systematic and the easiest to get hold of in any tradition: clear methods, clear stages, plenty of translations.
For reading, start with a selection from the Majjhima Nikāya, or go straight to the modern talks of Mahasi or Ajahn Chah. But read the risk notice on the method library page before you decide to sign up for a ten-day course. The intensity is not low, and the research on adverse effects comes mainly from exactly this kind of intensive setting.