What is the best way to structure a paragraph within an analytical essay?

There are many ways to structure a paragraph within an essay. Personally, before I start writing the essay, I make sure that I have played out a basic plan of the argument I wish to present. Through this you can prioritise and isolate what needs to be said, and which points contribute most heavily for your point. I always tend to start with a strong point and end with a strong point, with around 3-5 points depending on the question and the time allowance that you have.
When it comes to the structuring of the paragraph itself, I always find a P-E-E-L structure tends to be advantageous. The 'P' stands for Point - this is where you will state a subject sentence, that will show why this point contributes to your argument and also explain the point in as much detail as you feel necessary. Just because the acronym only contains four letters, does not mean that it has to be four sentences; it can be as many sentences as you feel necessary to communicate coherently and effectively. Following your point, you must present evidence in order to enforce the argument that you are attempting to make. This should be a quote either about character, theme, motif etc. Then you must explain your point in more detail - it would not be enough to just state your point and show evidence. If secondary criticism, historiography or a philosophers school of thought are needed within this essay, this is where you put it. Finally you end the paragraph with a link to both the initial argument you made at the start of your essay and paragraph, whilst also linking to the next paragraph demonstrating fluidity within the essay itself.