As long as the wood is dry and you have good kindling, does it matter how I start a fire?
All are perfectly valid, which works best depends on the circumstances.
In my experience a log cabin stack is good when you have short square sticks, for example what you would get from splitting sawn logs and a teepee tends to be easier to build when you have more irregular branches and twigs.
The lean to is useful if there is a strong wind coming from one direction and you want to use a log, rock or earth bank as a windbreak.
Really this only matters when you are laying the fire ready to light as you are trying to protect your kindling from wind and rain and make sure that the updraft is carrying the heat into the rest of the fuel. This really comes from having a sense of how a fire in general and the specific fuel you are using works.
In practice, in anything less that ideal conditions you need to pay close attention to how the fire is developing and add or remove fuel and adjust the structure accordingly.
Once the fire is properly going it just becomes a case of laying on the fuel to get the sort of heat you want. In a wild camp you want to just use what you can find as it is rather than spending time and effort processing it to conform to some arbitrary design of what a fire should look like so it is often a case of fitting in the odd shapes and sizes of fuel that you have to hand.
It honestly depends on conditions and what you are trying to accomplish.
If you have nice whittled shavings to start with, the make a log cabin of those, and slowly increase the size of kindling and finally logs added to the fire.
If you have branches that are roughly 1 inch, then a teepee is better.
Don't forget the star configuration. That 5 logs laid out radially, with a fire started in the center. As they burn you push the logs in closer to each other. It's perfect for cooking because you can control the heat, and it can maximize the lifetime of your fuel.
There are lots of configurations depending on conditions like the dryness of your firewood, how big it is, is it split or solid, what are you going to use the fire for. Do you want smoke or smokeless, do you want lots of heat or do you just want light to keep animals away, etc etc etc.
It's really too broad a question without knowing what you want to accomplish and under what conditions.