'The dating of [Dr] Faustus is an enigma and its textual history a maze. The earliest recorded performance on 30 September 1594, over a year after Marlowe's death, was certainly not the first. The earliest known printed edition (1604) may not have been the first either; the copy had been entered at Stationers' Hall three years previously. A different and longer text was published in 1616. The relationship between these two versions (known as the ‘A-text’ and ‘B-text’) is controversial. Some of the material unique to ‘B’ is probably by Samuel Rowley and William Birde, who were paid £4 for ‘adicyones in doctor fostes’ in 1602 (Henslowe's Diary, ed. W. W. Greg, 2 vols., 1904–08, 1.172). ‘A’, long considered inferior, is now thought closer to Marlowe's original text; some of its structural defects may be the results of censorship' as William Empson argued in Faustus and the Censors. (Charles Nicholl, Oxford Dictionary of National Biography)
Although the first performance references are to the Lord Admiral's Men's repertoire at the Rose in 1594 - with Edward Alleyn in the lead, these indication that the play had been performed at least two years earlier. According to Simon Trussler, 'the Admiral's are conjectured to have purchased the prompt-book from the company of Pembroke's Men which may have performed the play at court during the Christmas celebrations of 1592, and possibly at the Theatre in Shoreditch during a brief abatement of the plague in 1593.' (Simon Trussler, Dr Faustus - RSC Programme, 1989)
As for the dating of the play's composition, the jury is still out: if some scholars argue that The Tragical History of Doctor Faustus has been composed around 1592 - at the peak of Marlowe's dramatic career, others believe it followed shortly after the composition of his Tamburlaine, thus dating back to 1588/90.
Here's a selection of electronic editions, most of which are available via University of Warwick library subscription:
Dr Faustus (1604) available from LION
Dr Faustus (1616) available from LION
Dr Faustus (1631) available from EBBO
Dr Faustus (1663) available from EEBO