The main sources I have used for the history of ancient Rome are:
Stobart, J.C., The Grandeur that was Rome, Sidgwick & Jackson, 1961, a brilliant survey of Rome’s history and civilization for the general reader.
Flower, H.L., The Cambridge Campanion to the Roman Republic, CUP, 2004 – an excellent resume of recent scholarly studies.
Cowell, F.R., Everyday Life in Ancient Rome, Batsford, 1961 – a beautifully written and very accessible guide to daily life.
Talbert, R.J.A. (ed.), Atlas of Classical History, Routledge, 1985, p. 82ff. (for the Roman world): a detailed survey of the geography of Greek and Roman civilization; aimed at students rather than the general reader.
McEvedy, C., The New Penguin Atlas of Ancient History, Penguin, 2002, p. 72ff. (when Rome starts to appear). Despite its title, this small book, with its lovely clear maps, only covers the ancient West.
Haywood, J., The Penguin Historical Atlas of Ancient Civilizations, Penguin, 2005, p. 106ff. The section on Rome covers its history up to the 4th century BC (i.e. well before its major expansion).The text and the maps are excellent.
Grant, M. (ed.), Greece and Rome: the Birth of Western Civilization, Thames & Hudson, 1986: a lavishly illustrated book, with texts by some of the foremost classical scholars of the day.
Mosse, Claude, The Ancient World at Work, Chatto & Windus, 1969 – a sholarly look at the fundamentals of ancient Greek and Roman economics and society.
Burn, A.R. & Edwards, J.M.B., Greece and Rome, Scott, Foresman & co., 1970: a short, succinct overview of Graeco-Roman history. The section on Rome starts at p. 96.
Connolly, P., The Ancient City: Life in Classical Athens and Rome, OUP, 1998: a beautifully illustrated look at everyday life in these two cities. The section on Rome starts at p. 105.
For an overview of the archaeology of ancient Rome, I found the following useful (and enjoyable due to its lavish illustrations): Renfrew, C. (ed.), Past Worlds: The Times Atlas of Archaeology, Times Books, 1995, p. 168ff.
A work on general archaeology aimed more at students, but readable and with very good coverage of ancient Greece, is Scarre, C. (ed.), The Human Past, Thames & Hudson, 2005, p. 505ff.
For an insightful look at government in ancient Greece, especially at how Athenian democracy worked, see Finer, S. E., The History of Government, I, Ancient Monarchies and Empires, OUP, 1999, p. 528ff.
For specific aspects and periods of Roman history, I have found the following very useful:
Syme, R., The Roman Revolution, OUP, 1939 – a brilliant insight into the fall of the Republic
Cowell, F.R., Cicero and the Roman Republic, Pelican, 1973 – a wonderful study of the last age of the Republic
Scullard, H.H., Roman Politics 220-150 BC, OUP, 1951 – a detailed examination of politics in the middle Republic; not for the faint-hearted.
Adcock, F.E., Roman Political Ideas and Practice, University of Michigan, 1959 – an overview of this subject.
Birley, A.R., Life in Roman Britain, Batsford, 1964 – an accessible survey for the general reader.
I make no apology for many of these sources being several decades old. If you want to read a recent treatment of Roman history, the following have been well-received:
Beard, M., SPQR: A History of Ancient Rome, Profile Books, 2015
Baker, S., Ancient Rome: the Rise and Fall of an Empire, BBC Books, 2007
There are huge numbers of sites on ancient Rome. From my research probably the most useful are these:
The Ancient History Encyclopedia has good articles on Ancient Rome
Wikipedia has a vast amount of information on Ancient Rome