If you want to start at the beginning, you should probably look at the Illiad and the Odyssee. They will also give you a lot of context and knowledge about the gods and the culture. Then you could continue with Herodotus and Thucydides. These are about the classical period in ancient greece. For the romans the first source we have in a higher quantity is Polybius. He talks about the punic wars up until the third, which is the time at which he writes. These are all sources that write from their respective perspective and you should always take whatever they say with a grain of salt. If you want to delve deeper into their time periods it is probably a good idea to read some modern historians books.

You can still read the sources and just try to read in between the lines yourself. This is pretty fun and you are basically doing what historians do as their job.