How can you figure out what you believe about history as well as where you stand politically these days?
Well, you can make a value judgement about everything. I do, but I also try to remember that my views will change as I learn more. Just keep reading, thinking, discussing and debating. If it's a secondary source, find out who paid for it, who they wrote it for, and what their agenda was.
For history, I hear about reading primary sources, but aren't they still biased?
Definitely! But if you can figure out where there bias lies, you can make some pretty safe assumptions. Thucydides writes some very informative stuff about the Persian and Peloponnese wars, but being Greek, it's a given that there will be some bias in favour of his home country. There's nothing you can do about this, except, if possible, find sources from another perspective, and then compare. Remember too, that a primary source is considered valid if another separate primary source corroborates it. If you can find three primary sources of
different origins backing up the same info, then you're probably onto something good.
Just because a source is biased, does not mean it isn't useful. Josephus wrote about Jesus' crucifixion from a non-believing perspective (if I remember rightly) but what he wrote still provides valuable insights into what may have been a popular Jewish stance at the time.
We know his opinion is false, but we can still learn something from what he wrote.
How can you tell whether a person's quotes/beliefs are taken out of context by someone trying to spin his own agenda?
If you really want to know, it might take a lot of digging. Sometimes it's clear, but other times, you will just need to keep searching if you really want to know for sure. You can get lost in that stuff!
One source may say that a person was a great Christian, but another source has quotes or articles stating otherwise.
Look at their actions and what the consequences were. Still, you may never know for sure, and it's probably not important (for you!) whether they were or not.
I think the question is how determined are you to find out the truth about something? How important is it to you and your family?
Archeologists/historians/history buffs can devote their whole lives to that stuff and still draw blanks. Some things we will just never know.
It is fun and good to find out more than the average history book wants to tell you, but I wouldn't sleep over wondering whether or not st.Augustine was a genuine convert or not.
And it's awesome for your opinion and understanding of things to change over time. Nothing wrong with that

Hope that helps !