I wish I had a short easy answer. I've found most history books, articles and translations written after 1950 have a gradually increasingly anti-western bias, accelerating greatly around 2010. That in mind...
Sourcebooks can give a good overview. They're a collection of primary sources orientated around a particular subject. Almost like a catalogue that you can easily flip through.
They're especially useful because they often include fragments, inscriptions, artifacts, and artwork in addition to a variety of written records which gives a fuller picture.
For more in depth understanding, read works written during the era of interest. Don't rely on someone else's interpretation, go directly to the source or as close to it as possible.
Many old 'outdated' translations of important primary sources are available for free online on various university history department pages.
Once you have a good grasp of a chosen time/place/topic you can easily build and branch out from there.
You'll also be better able to gauge the trustworthiness of more recently written history books because you'll be able to catch lies and half-truths when they dip your area of study.
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