I currently have the choice of two routes with my novel - to lead with a knives-and-poisons main conflict, with reference to the protagonist's emotional conflict, or to lead with him conquering his inability to manage his peculiarities (OCD, etc) while untangling the plot. I understand that both will influence the other, but is there a best practice with which one to lead with?
The heart of a story is neither physical conflict nor emotional conflict, it is moral conflict. That is to say, it is about the character being made to face a choice about values. Does pride and prejudice win out over love? Does Spiderman save MJ or the busload of children?
Emotional conflict results from moral conflict. Moral conflict forces us to pay a price to attain a goal. There is an emotional cost to paying the price and an emotional gain from achieving the goal.
Physical conflict arises because two characters have different, non-compatible goals. This poses another moral conflict -- am I willing to engage in violence to achieve my goals.
So, in the hierarchy of conflicts, moral conflict is at the top, emotional conflict is in the middle, and physical conflict is at the bottom. Physical conflict alone is not very interesting. The interest comes from the emotional conflict and, more fundamentally, the moral conflict.
This does not mean that you have to do a full exposition of the moral conflict, followed by a full exposition of the emotional conflict, followed by a full exposition of the physical conflict. But it does mean that the reader needs to see at least the seeds of the moral and emotional conflict before you can expect them to engage with the physical conflict.
I think that depends entirely on your story and the initial mood you're trying to establish (both for the story and between the characters). Starting with a physical conflict is a fairly easy way to quickly draw your reader in. It's the cheapest way of creating dramatic circumstances: Raise your reader's pulse quickly in order to demand their focus.
If you start with an emotional conflict or backstory, you gamble a little with their interest in that plot line. It's harder because this way you need to convince the reader that this is both dramatic and interesting, while two dudes fighting or a battle scene does that almost implicitly.
So what should you start with? Well, what is the tone and speed of your story? Start high quickly (and then take the reader on rollercoasters) or slowly build up and increase tension over the course of the first act?
The final answer to your question is: There is no "best practice", just what suits your particular story progression.
I think the really important conflict is between the world inside a character's head and the world outside of it. Since "the world outside of it" is usually shaped by other characters acting in accordance with their own model of the world, this almost always has a moral dimension (because that model of the world will include a model of how people should behave in it), a physical dimension (because they will physically interact with things) and an emotional one (because they will have invested their emotions in aspects of their world model).
My view is that a story is, at its simplest level, about a character encountering something that doesn't mesh with their understanding of the world, and having to make a choice between changing the world or changing themselves. A story generally ends when the relevant aspect of the world and the relevant aspect of the character's understanding of it are in alignment.
So, think about who your character is, what they believe and what they want, and think about the sort of conflict that really defines the start of their story arc. Whether that ends up being physical or emotional is usually irrelevant; it's how it relates to the overall story that really matters.
I think that depends entirely on the nature of the story.
At the extreme: If the story is all about a person's emotional struggles, throwing in a gratuitous fight scene to try to grab the reader's interest seems counterproductive to me. It will mislead the reader about the nature of the story and put him in the wrong frame of mind.
Even if the story includes both physical conflict and emotional struggles, if it's mostly about the emotional struggles and the fighting is an outgrowth of that, starting with a fight scene might be a way to begin with high drama, but it could also be misleading and distracting.
I suppose it's easier to grab a reader's attention with a fight scene. You don't need to know much about the characters to understand it. A scene about a character's emotional struggles may require some background. But not necessarily. A story that began, "Bob decided that his only choice was to kill himself" would probably grab the reader's attention without knowing anything about Bob. Indeed if I read that as the first sentence of a story, I think I'd immediately be asking, "Why does Bob want to kill himself? What happened to him?" etc.
I'd add that in my humble opinion, fight scenes and car chases and the like work very well in movies, but not nearly so well in books. It's hard to capture the action and tension with printed words. Not impossible, but hard. I often find myself skimming over fight scenes in books with a "yeah, yeah, I get it, they had a fight".