The best source for the text of this work is the De Lacy translation available here. The appendix is excellent and should be read, if possible, before the work itself.

"On Methods of Inference" - Best Source for the Text And Getting Started
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Cassius
Changed the title of the thread from “"On Methods of Inference" - Best Source for the Text” to “"On Methods of Inference" - Best Source for the Text And Getting Started”. -
The beginning sections of the text are not preserved, and therefore we don't have the opening explanation for what the work is about in order to serve as a guideline for what follows.
Perhaps even worse, the work includes lots of repetition of positions that Philodemus is arguing *against*, so it's necessary to know beforehand which side of the argument Philodemus is taking so that you know if he's talking about his side, or that of the (largely stoic) enemy.
And perhaps even worst of all, the Epicurean arguments are so unknown to us that it takes considerable explanation to understand the Epicurean side of things before getting started.
So for that reason I strongly recommend reading the introductory material, and the appendix, before reading the text itself. Of course that means we're relying on DeLacey, and we have to be careful about that too, but it's better than starting at the beginning and reading pages and pages of dense material and only finding out afterward that you've started in a section giving the Stoic argument and that Philodemus himself doesn't agree with anything that you've just read.
Here are some links to the sections to read first. Every one of these contains valuable information that will help tremendously if you read it before reading the text.