The New Edinburgh History of Scotland series, edited by recently retired Scottish historian Roger Mason, breaks the history of Scotland down into several chronological chunks. Each book in the series is written by an expert in the period. Right now all periods are covered except for 1372-1485 and 1588-1790, which are admittedly very important eras in Scottish history! While the books are written by academics, they are meant to be accessible to the general reader too. https://edinburghuniversitypress.com/series-new-edinburgh-history-of-scotland.html

• James Fraser's From Caledonia to Pictland: Scotland to 795 covers the Iron Age, Roman Britain, and the early medieval period. This book was a huge landmark publication because it was the first book to attempt to write a really detailed and rigorous political history of the earliest period in Scotland's history.

• Alex Woolf's From Pictland to Alba: 789-1070 covers such topics as the Vikings in Scotland, the unification of the kingdom of Alba (the earliest united form of a Scottish kingdom), and interactions with the Northumbrians, who still ruled part of what is now considered Scotland.

• Richard Oram's Domination and Lordship: Scotland 1070-1230 deals with the Anglo-Norman period in Scotland's history, a time of greater influence from the Continent through figures such as Queen Margaret of Scotland. The book also covers the development of towns and cities, changes to the nobility in line with Continental developments, and the church reforms that affected Scotland in this period.

• Michael Brown's The Wars of Scotland: 1214-1371 covers the period of Scottish wars of independence against the English. Famous figures such as William Wallace and Robert the Bruce are covered here.

[No volume yet covering 1372-1487, which includes the foundation of the Stewart monarchy and the wars between the Scottish kings and the Lords of the Isles, which eventually led to the Hebrides and the Highlands being incorporated into the Scottish kingdom.]

• Jane A. E. Dawson's Scotland Re-formed: 1488-1587 covers the late medieval period, including famous Stewart monarchs like Mary Queen of Scots. The big topic here is the Scottish Reformation, when Scotland broke from the Catholic church in 1560 and started following a radical Calvinist form of Protestantism developed by John Knox. Mary Queen of Scots was executed in 1587, and she was the last Scottish monarch who did not also rule in England. The vast majority of Scotland's medieval art was destroyed during the Reformation. After the Reformation, widespread education began to increase literacy levels across the country.

[No volume yet covering 1588-1789. This was a hugely important period for Scotland's history. The Scottish monarch moved to London with James VI and I in 1603, and the Union of the Crowns dissolved the Scottish Parliament in 1707, unifying Scotland and England into one kingdom. More radical forms of Protestantism such as the Covenanters caused huge religious conflict in the country which often ended violently, since they were outlawed by the state. After the Glorious Revolution in 1688, which dethroned the Catholic Stewarts from the joint English and Scottish throne, the Jacobite movement rose to great prominence in Scotland. The Jacobites wanted to restore the Stewart line. Led by Stewart pretenders such as Bonnie Prince Charlie, they had military victories in the 18th century but were ultimately defeated at the Battle of Culloden in 1745. The British state then intervened in the Highlands to break down traditional societal structures, outlaw aspects of Scottish culture, and enforce English-language education to the detriment of Scottish Gaelic. During this period, Scotland also started participating in imperialism and colonialism abroad in places like the Caribbean, taking full part in the trans-Atlantic slave trade. Also of huge relevance here was the Enlightenment, with many inventions and philosophical developments originating with Scottish thinkers. Most famously, Adam Smith's book An Inquiry into the Nature and Causes of the Wealth of Nations is popularly considered to be the foundation of modern capitalism. Poets like Robert Burns and Carolina Oliphant, Lady Nairne, represent the flourishing of Scottish literature at this time.]

• Iain Hutchison's Industry, Reform and Empire: Scotland 1790-1880 covers the industrialization of Scotland. Glasgow in particular was a key industrial city of the British Empire. Hutchison will cover people's greater participation in the political process and the Disruption of 1843 which saw the establishment of the Free Kirk. This period also saw the height of the Clearances, a massive depopulation of the Highlands instigated by landlords who found it more profitable to have sheep on their land than farmers. The Clearances coincided with increased military and government presence in the Highlands after the Jacobite wars and led to mass emigration of Gaels, particularly to Canada. Many also moved to Glasgow, contributing to its development as an urban powerhouse.

• Ewen Cameron's Impaled Upon a Thistle: Scotland Since 1880 rounds off the series bringing it forward from Victorian times to the modern day. Cameron focuses on political developments such as the rise of socialism and nationalism in Scotland.

Now, all the books I've listed above are about specific time periods, not Scotland's history as a whole, which is admittedly what you asked for. For a popular overview of Scotland's history, Neil Oliver's A History of Scotland from 2010 is probably your best bet. I can't vouch for its scholarly accuracy on all fronts as I haven't read it myself, but it would give you a great overview of Scottish history. Then you could dive into one of the more specific volumes above if you wanted.

There's also recently been a growth in books about the history of women in Scotland, a hugely neglected field. I haven't read it yet, but Rosemary Goring's Scotland: Her Story: The Nation's History by the Women Who Lived It (2018) looks promising. So far I am enjoying Sara Sheridan's Where are the Women? A Guide to an Imagined Scotland (2019), which takes you on a tour through Scotland as if all the monuments, streets, museums, etc. were dedicated to women instead of men. It's very thought-provoking and I'm learning a lot, but it's probably best saved for when you have a better idea of Scotland's history and geography.

The Last of the Free: A Millenial History of the Highlands and Islands by James Hunter is a very good overview of the region, and written to be accessible and easily understood by people with no background or training in history. It makes a fantastic starting point to learning about that area of Scotland.

Another one with a similar focus, but more narrowly on Gaelic history would be Warriors of the Word: The World of the Scottish Highlanders by Michael Newton. It is also a good overview, though not as accessible as James Hunter's writing. It's very interesting for insight into traditions and language as well as politics.

I'm afraid I don't have anything "general overview" on the development of the Kingdom of Scotland, though, as my focus really is and has ever been Gaeldom and the Highlands.