The obvious commercial options are Volley and Bayonet, Principles of War, Warring Empires and Wars of Empire. The Fire and Fury Francesa variant is good, also Nineteenth Century Wargames by Neil Thomas and Barkers Horse, Foot and Guns.
I have tried all these, and many more, so ultimately it depends what you are looking for in a game. It was a war of extreme asymmetries in weapons, tactics, organisation, command and control and the philosophy of war, and to recreate it, you need to capture some of that. It is also a war on two levels, many of the actions were Corps sized, so happily easily resolved using rules with battalions or regiments as the element of Manoeuvre, but the major battles (notably Custoza and Koeniggratz) were gigantic multiple corps/army affairs which warrant different handling.
I do it in 6mm, so that that I can use the same stuff for 1859, 1866 and 1870 which also means my Austrians get to fight in their nice white Kittels, so much smarter than those horrid greatcoats.
If you want a simple set to get started, give Neil Thomas a go.
"Mistakes in the initial deployment cannot be rectified" - Helmuth von Moltke