So there are a few major historical periods one could look at. Generally speaking there's not that much in the way of really good narrative histories for most of it, because documentation is sparse. I'll give you a few suggestions for things to read (based on the well known methodology of "looking through my bookshelves").

On the Achaemenids:

• The Persian Empire by Amelie Kuhrt. This is a massive corpus of sources in translation, and is a very good way of getting a solid overview of what we can actually know about the Achaemenids.

- King & Court in Ancient Persia and The Persians by Lloyd Llewellyn-Jones. Good recent terse overviews. LLJ is particularly into things like art, clothing, cuisine, etc, so especially if you like those things he's a great read.

ETA: See /u/Trevor_Culley's comments below, Maria Brosius' recent work on the Achaemenids is a better choice for an overview.

On the Sasanians:

• Sasanian Persia by Touraj Daryaee. Great overview of the Sasanians, and eminently readable.

• Decline and Fall of the Sasanian Empire by Parvaneh Pourshariati. A big tome that presents Pourshariati's thesis of the "Sasanian confederacy", and how that lead both to its long prosperity and its decline.

On the Timurids:

• Power, Politics and Religion in Timurid Iran by Beatrice Mantz. The Timurid period was foundational for later periods, so this is a rather good (if a bit dry) read. Probably only worth it if you already have an interest in the period.

Safavids:

• Mystics, Monarchs and Messiahs by Cathryn Babayan. This is a bit of a tough read but it explains the general cultural milieu that gave rise to the religious fanaticism of the Safavids, which in many ways lives on to this day. Not a good intro in itself, you may wish to read an overview work on late-post Timurids-early Safavids first, but I don't have a good recommendation there.

I have a more suggestions for more niche stuff on the ancient era, but that's probably not what you are looking for right now. If you're interested in pre-Islamic religion, read Jenny Rose's Zoroastrianism: An introduction. For ancient oral tradition and Middle Persian literature, M. Rahim Shayegan has some classic texts about that, but bear in mind that they are extremely dry reads.

There's of course the pre-Mongol half of the Islamic age, but I don't have any great suggestions for that.

I hope this helps a bit. There may be more recent works that I haven't paid attention to; I've been doing my PhD for a few years and mostly read about Chinese history, so I'm not as up to date as I could be.