Short answer:
Slightly longer answer:
The most recent major discovery of Sappho’s works was in 2014, when new fragments of nine poems – including one entirely new poem, almost complete – were published. If you want to read a translation of Sappho’s complete works today you want one which contains these discoveries. Four major translations in English do this:
Of these, my preference is Rayor & Lardinois, followed by Lombardo; Powell is my least favourite. Realistically all of these are probably fine for most readers.
Before the 2014 discoveries, the most commonly recommended translation of Sappho was probably Anne Carson’s If Not, Winter (2002). Her translation is excellent but given the now-outdated texts of several important poems and the fact that it is missing the “Brothers Poem” entirely I would not recommend it when any of the four recent translations is available. If you desperately need a translation with facing Greek text, and are willing to sacrifice the 2004 and 2014 discoveries to get it, then this is an excellent option. Alternative translations with parallel Greek text include David A. Campbell’s Sappho and Alcaeus (reliable prose translations of both Sappho and her contemporary Alcaeus; a good selection of ancient sources about the poets) or Willis Barnstone’s Sweetbitter Love: Poems of Sappho (more recent and incorporating the 2004 discoveries for the text of fr. 58, but now out of print; his 2009 The Complete Poems of Sappho has the same translations but does not contain the parallel Greek text).
Another translation which is widely recommended online is Mary Barnard’s Sappho: A New Translation. This was an enormously influential translation in its day but it was first published in 1958 and it is massively outdated. There are good reasons to read Barnard but you should be familiar with a more reliable modern translation before you pick this up.