It depends on whether you are interested in lifetime editions or posthumous editions. There are, for example, three lifetime editions of Mary Shelley's Frankenstein (1818, 1823, and 1831); but there are hundreds of posthumous editions, variously based on these three. What makes a lifetime edition preferable is a very different set of factors than what makes a posthumous edition preferable.
Assessing a lifetime edition involves several subjective and objection considerations. The main subjective consideration is which edition seems to best express what the author was going for. There is general agreement among modern scholars, for example, that the 1802 edition of Maria Edgeworth's Belinda is a more faithful expression of her intentions than the 1810 edition, from which she eliminated an inter-racial marriage due to critical backlash. Other cases are more ambiguous. Are we interested in the author's original vision or in their more mature re-envisioning of the work? That, again, is subjective and depends on your reasons for reading that particular work. Some scholars prefer the 1818 version of Frankenstein, while others prefer the third, 1831 edition. More objective considerations include whether the edition is clean or full of printer errors, whether there is evidence that the author got to see it and revise it, and so on.
Assessing a posthumous edition is a completely different affair. When I'm looking for a good modern edition of Frankenstein, I am interested in the quality of the critical apparatus -- the introduction, the notes, any appendixes. I am also interested in who prepared the edition; was it prepared by a professional scholar on the basis of lifetime editions, or just taken from the internet by the press? A good posthumous edition should explain which lifetime edition it is using, and ideally also explain the differences between lifetime editions as well as the reasons for choosing one over the others. The Oxford World's Classics series, for example, always includes a "Note on the Text" giving an account of the lifetime editions and the editor's decisions. Editions of Shakespeare should be particularly explicit in this regard, as editing Shakespeare's plays often involves combining different existing versions into a compound. A modern edition of Hamlet is usually a mixture between three early editions.
The best place to identify lifetime editions prior to the 1800s is the English Short Title Catalogue: http://estc.bl.uk/F/?func=file&file_name=login-bl-estc. Which edition is best varies by case, and the only way to figure that out is to consult the specialized literature on that particular item.
Determining which is the best posthumous edition involves research of a different type. For many authors there is a "standard" modern edition that scholars tend to prefer. For Austen, that's the Cambridge edition; for Samuel Johnson it's the Yale edition. A good paperback (say, Penguin, Norton, or Oxford) should tell you what the standard edition is. Most readers don't need the standard edition, which is expensive and targeted at academic libraries rather than individual readers. For most of us, a good paperback with an introduction and notes is good enough.