Here's a thing you need to consider, a frame challenge if you will.
When setting your story in the 1950s, or in the 1920s, or even in the 1800s, your characters can speak the way people spoke back then. In fact, we rather expect them to.
But if you set your novel in Shakespeare's time, and one uneducated street child tells another "thou art a boil, a plague sore" (King Lear Act 2, Scene 2), the readers would struggle with it. The thing is, back in Shakespeare's time, a child might indeed have used just these words. But to your modern reader, they are perceived as antiquated, and for that reason - high-brow.
What you want to recreate is not how a character of the given period would have sounded, but how he would have sounded to his contemporaries. Which would imply using language that is perceived as "normal", "vanilla" rather than period-specific.
But a character's "voice" is not just the language he uses. There are other elements - how he thinks of himself and of others, how he perceives the world around him, what his reference points are, what metaphors he would use. Relevant to this is not only the character's time period, but his position in society, level of education, his opinions (from within the range available in any given time and place).
To get an idea of those elements, you can look at literature written in the time period that interests you. You can look at scholarly works about that period, if you find something relevant. You can look at literature that was written slightly later, to see how that period looked at the previous one - what changed would emphasise what was before. From some time periods, there's published correspondence of famous figures. In later periods, there's newspapers and interviews. There's an ongoing effort to digitise those sources, which makes access easier. You might also find it useful to visit museum exhibitions: there's a lot objects can tell you about the people who used them - about what they deemed necessary, and therefore how they viewed the world.
As @B.L.E states, getting access to actual letters, diaries etc. would be extremely difficult: since those sources are very fragile, you'd need to attain permission to view each individual source, which is a complicated process even for accredited scholars who work in the field, much more so for someone coming from outside.