Psychology and neuroscience are your best bets for answers. Philosophy can speculate on questions that those two have not answered, but it is best for you to look at the answers before you start examining the questions.

Makes sense, thanks for pointing the way.

What influences our thoughts? That somehow feels wrong to me. It's not that there are influences as much as it's a question of exploration of ideas/concepts/theories. Granted some of what one encounters in the journey through the idea jungle rubs off on us in that they shape certain worldviews but that misses the point doesn't it? In a journey, there's the traveler and then there's the places fae travels to and they're not the same.

Wouldn't the answer depend a bit upon which thoughts one has in mind and when one asks the question?

Influences as in the things that go into making the subjective experience of viewing the world from one's own perspective.

Let me give you an example, I grew up in a fairly liberal household where I was encouraged from an early childhood to question everything. I was introduced to the scientific method and the skepticism that comes with it. One of my friend has become a fundamentalist who is convinced that god is pulling the strings behind everything and is for some reason convinced that science is just a lie that satan is playing on the unsuspecting men and women. This brings up the broader question of what constitutes reality? is it something physical or purely mental or something in between? or is my ape brain getting way ahead of itself by projecting some neurochemicals inside my skull onto the world by assigning arbitrary meaning to whatever it is that I see, feel and experience?

In the words of Stephen Jay Gould "The human mind delights in finding pattern—so much so that we often mistake coincidence or forced analogy for profound meaning. No other habit of thought lies so deeply within the soul of a small creature trying to make sense of a complex world not constructed for it."

This brings up the broader question of what constitutes reality? — Aristotle21

Is the answer supposed to be something easy to understand, perhaps a list of a few factors or a single factor?

What if this is an answer that continues to present itself in a new manner as one simply receives more and more information over time; thus refining this answer never allowing it to be a fixed point?

What if the answer ends up as 'everything'?

I'm not completely sold with the notion of the human mind 'delights' in finding patterns. It would seem that pattern seeking is a key to survival and 'delights' seems a bit too much like the humans are out on a lark having fun just for kicks.

What are things?

Aren't things in the end simply a collections of matter that we recognize in some sort of consistent manner and thus grant them a value and a name?

It's quite useful to recognize if something is food and not toxic as to continue living rather than dying, so I'm not sold of the 'delights' aspect.

Anyway... the Gould quote reminded me of this, for what it's worth:

We constantly create false positives, we touch wood for luck, see faces in toasted cheese, fortunes in tea leaves. These provide a comforting illusion of meaning. This is the human condition we desperately want to feel there’s an organizing force at work in our bewilderingly complex world. And in the irrational mind set if you believe in the mystical pattern you’ve imposed on reality, you call yourself spiritual.
― Richard Dawkins

I'm very curious about what factors lead to how a person thinks — Aristotle21

The electro-chemical information medium all ideas are made of. All thoughts, philosophies, ideas, opinions etc inherit the properties of the medium they are all made of.

That's the primary factor of influence. The rest are little details.

As far as I see it, the issue is how to focus thoughts. Some people dwell a lot on the past. I am inclined to worry about the future too much. I do tend to think a lot about the previous day whenever I wake up. It can be so easy to dwell on the little details of one's own life. Most days I try to read straight after breakfast as this enables me to direct my focus away from my own concerns. I like to dip in and out of a few different books, usually a mixture of fiction and dare I say it, a bit of philosophy.

Your core question seems to be about what factors affect the thinking in the first place which is more about thinking disposition. Of course, some people tend to think about certain things. It is probably the case that brain development does influence this. For example, some people are born worries whereas others are optimistic. But I am inclined to think that we choose what we think about.

In particular, while brain chemistry affects people who are depressed and is likely to lead to negative thoughts it is likely that the negative thoughts give a feedback loop and give rise to further depression. So it is important what we focus upon. It is difficult though, especially if alone for long periods of time.

I think we can achieve more consciousness direction in thinking through mindfulness. I don't practice it always but I have found some techniques helpful. However, that is not about switching off from thoughts but often about direct experience of the senses and it can be about observing one's own thoughts, which is about a certain distancing from them.

So, I am saying in answer to your question while certain brain chemistry probably influences the agenda of our thought we have a fair amount of freedom to choose what we focus upon. This freedom is a positive part of life because it gives scope for us to create and maneuver inner experience rather than simply be overwhelmed by any strand of thought entering conscious experience.

I expect some people are more image based whereas others think more verbally. But all of this can be moderated by us.