I'm very happy to answer your question as asked, but before answering it I do want to give you one caveat- Herodotus is still a useful source on the Persian Wars and a number of other things, but when used cautiously. As you might imagine, both 300 and its sequel diverge enormously even from the probably exaggerated account of Herodotus. That being said, it is true that one should never just use Herodotus, or even primarily use him, as a source for the Persian Empire. When approached with sufficient caution, and understanding of what Herodotus is useful for, his work can be a goldmine. But that does involve a lot of source criticism, and probably reading of commentaries on Herodotus, and you're likely looking for more accurate information more immediately (and with a modern audience in mind).

So, with that said, there are a number of works I'd recommend on introducing yourself to the Achaemenid Persian Empire.

• In terms of books specifically on the Achaemenids, From Cyrus to Alexander: A History of the Persian Empire, by Pierre Briant was for me the standard introduction. Perhaps a difficult one to get hold of, but it is still one of the most comprehensive modern analyses of the Achaemenids. Briant is fairly sweet on them, so bear that in mind. Additional books solely on the Achaemenids include: The Persian Empire: a history by Lindsay Allen; and also the (imaginatively titled) The Persians by Maria Brosius.

• Wide-overviews of Ancient Near Eastern history deal extensively with the Achaemenids and their immediate context, including: A History of the Ancient Near East ca. 3000-323 BC by Marc van der Mieroop; The Ancient Near East c.3000-330 BC by Amelie Kuhrt. Both of these are good, solid introductions to the Near East generally as well.

• Webwise, Achemenet has a huge database of things relating to the Achaemenids. It has both a French and English version, with one big caveat- the site is a bit awkward to navigate. Additionally there's Encyclopaedia Iranica, which has a much bigger library of Achaemenid stuff than some others. However, when looking at an article there it is best to check it against other sources; due to beiing relatively low-traffic, it's relatively easy for a few of the articles to have some slightly dubious statements hidden in them.

• If you have the time and inclination for source books, The Persian Empire: A Corpus of sources for the Achaemenid Period by Amelie Kuhrt collects almost all extant sources on the Achaemenid Empire from various periods and places (ancient ones though).

This is just the tip of the iceberg. There's an entire discipline dedicated to researching and analysing the Achaemenids in their own right, and not via the lens of the ancient Greek sources (though they should never be thrown out entirely). For every book here there's probably 8-9 times that which I didn't mention by name, due to being too specific or too esoteric

Any one of the books I recommended (bar the source book) would stand you in good stead as an introduction to the Achaemenids. Even better would be more than one of them, but given that your libraries nearby might not be all that great, or they might be financially unviable for you to buy, don't feel that you should own many or all of these books.