Read Herodotus and Diodorus together. Herodotus ends with the Persian wars, Diodorus covers the period until the Peloponnese war. When you reach that point, start with Thucydides and leave Diodorus. After that follow up with Xenophon's Hellenica. When you end up with Xenophon's Hellenica ctrl+F into Diodorus's work and write Agesilaus II or just Agesilaus until you find the paragraph, where he is in Egypt. For me, you can follow Diodorus all the way until the First Punic War - I think there was a lacuna on it (might be in Livy, don't really remember, but I think it was in Livy). So when you reach the First Punic War, open Polybius - you can read him until the end (destruction of Carthage - 146 B.C.) if you want a view of everything happening during that period, or you can go into more detailed writing of Livy (AFTER the First Punic War), but he reflects mostly on Rome and barely mentions the states of Hella (for example the exploits of Philip the V'th before his interaction with the Carthaginians via embassy). At 146 B.C. turn back to Diodorus (key word - destruction/ruin of Carthage or something like that) and follow freely until you reach the name of Jugurtha. Then leave Diodorus again and read the "Jugurthine War" by Salustius. With it ending, you can read Plutarch's works: "Life of Sulla", "Life of Marius" and Appian's "Civil Wars" (you can read only Appian's work if you don't want to track the conflict that heavily). Now, there is a HUGE happening, which you, in my opinion, must not miss - the Mithridatic war (Appian, but my favorite is Life of Lucullus by Plutarch... and maybe "Life of Pompey") Afterwards Plutarch's Life of Caesar + Caesar's own works - you must seek their chronology yourself, I forgot if he was in Spain before or after Egypt (might have been 2 times) - I just know his first is "Civil war". Together with them, start The Twelve Caesars by Suetonius and keep up with the chronology.
After Caesar, continue with Plutarch's: "Life of Brutus" and "Life of Antony" (the second one is very good detailed). Suetonius "The Twelve Caesars". Outside of Suetonius, I am not familiar with the life of Augustus, but if you want to read A.D. I'd recommend to you to start with Tacitus, on whom I currently am (haven't read since a while, but will start him soon again) :)
There are more sources, but on first thought this is what I came up with from Herodotus until the birth of Christ.
EDIT: All sources mentioned are available for free on the internet.