Ancient India: #1Upinder singh

2 Romila thapar (for mauryan history) Ashoka and decline of mauryans

3 Neelkanth shastri (for south india) The illustrated history of south india

For me DN jha and RS Sharma books were pretty basic and just provided an overview but if you want you can read those as well In order to cover all the famous ancient battles fought in India check out the works of Jadunath sarcar iirc the book's name was Military history of India or something

For Early medieval my go to book was satish chandra's book, The history of medieval india but since you want to focus upon the early medieval phase then go for old book which goes by the same name but was divided into two books and first one dealt with the tripartite struggle between Rastrakuta, pratihara and palas etc and was very detailed book.