These are good and varied collection of texts that you'd find on any decent university level course and are accessible to the layman:

• The World of Late Antiquity: AD 150-750 by Peter Brown
• The Fall of Rome and the End of Civilisation by Bryan Ward-Perkins
• The Fall of the Roman Empire: A New History of Rome and the Barbarians by Peter Heather
• Barbarian Migrations and the Roman West, 376-568 by Guy Halsall

Really anything on the /r/AskHistorians book list for late antiquity is good, modern reading (although Jones is something to only skim unless you're studying it in earnest).