An adventurous DM might want to try combining the Starter Set‘s Lost Mine of Phandelver, with Essentials Kit‘s Dragon of Icespire Peak into one big adventure: The Lost Dragon of Phandelver.
The former is ideal for a group of 4-6, and includes an adventure book with everything the DM needs to get started running the Lost Mine of Phandelver, a rulebook for playing characters level 1-5, etc.
978-0-7869-6683-7
(Dragon of Icespire Peak)
The latter contains the essentials you need to run a D&D game with one DM and one to five adventurers. A newly designed rulebook on-boards players by teaching them how to make characters, and the included adventure, Dragon of Icespire Peak.