As with all of Shakespeare's plays, thoroughly annotated critical editions are the most useful way to engage with early modern texts. For contemporary readers, Shakespeare's language is often considered difficult to parse, and the numerous allusions included in the text could be lost without proper annotation from a scholarly edition. These editions will contain footnotes that help explain particular vocabulary, usage, allusions, and relevant historical information.
Three editions were used in preparing this ClassicNote: the Pelican Edition, edited by A.R. Braunmuller, the Norton Critical Edition, edited by Robert S Miola, and the Arden Edition, edited by Ann Thompson and Neil Taylor. The Pelican is quite affordable and has a useful introduction to contemporary critical approaches. The Norton Critical contains an invaluable appendix full of past and recent criticism on the play. The Arden is the most exhaustive scholarly treatment – it sells for quite a bit more money but it can be readily found in most college libraries and is probably the best edition to use for writing college-level essays.
Many more comparable editions of Hamlet are available, including editions from Signet Classics, the Folger Library, Bantam Press, and several university presses (Cambridge, Oxford, Yale, etc.).