Ah yes, the question of sá-sí!
If you have access to The Peoples of Middle-earth, I recommend you read The Shibboleth of Fëanor, which explains this topic. But I'll explain the basics:
First things first: I would recommend using þ in spelling, regardless of how it is to be pronounced, if only because the Elves themselves retained the distinction in spelling. E.g. in the text of Namárie the words sí and sindanóriello (= þindanóriello) are to be spelled with different tengwar for their first consonants: sí and þindanóriello respectively.
As for the pronunciation and what The Shibboleth of Fëanor tells us:
At some relatively recent point in the historical development of the Quenya language amongst the Ñoldor many of them lost the distinction between the consonants [s] (as in English soup) and [θ] (written þ, pronounced as in English think, not as in that), and merged both into [s]. Not all Ñoldor made this change in their pronunciation; notably the House of Finarfin did not. More notably still Fëanor resisted this change, and even made it into a political issue.
Fëanor felt slighted by this change in pronunciation, primarily because it affected the sobriquet of his mother, Míriel Þerinde, meaning "Broideress, Needlewoman"; it is not plainly stated by Tolkien, but some Tolkienian linguists have observed that, if it is mispronounced as Serinde, it may be misinterpreted as a derivative of ser-, and thus mean "she who rests".
“[...] So Fëanor would call himself ‘Son of the Þerindë’, and when his sons in their childhood asked why their kin in the house of Finwë used s for þ he answered: ‘Take no heed! We speak as is right, and as King Finwë himself did before he was led astray. We are his heirs by right and the elder house. Let them sá-sí, if they can speak no better.’” [The Peoples of Middle-earth, The Shibboleth of Fëanor, p. 336]
The issue was indeed so political in the end, that Galadriel, though a member fo the House of Finarfin (who did not sá-sí to begin with), spoke with s in place of þ to spite Fëanor.
At the same time, however, þ has partly returned to Quenya following the exile, through the influence of Sindarin (= Þindarin), but that was mostly restricted to the recitation of literary texts. Loremasters, though, tended to speak with þ in their daily speech as well.
So to wrap up the answer - which may well be much longer than you bargained for - you may pronounce it either with [s] or with [θ], up to your preference. You may motivate your choice in various ways, if you want:
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For [s]: by taking a political stance against Fëanor, as Galadriel did; or by simply being one of the many speakers who simply spoke that way, as for example King Finwë himself.
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For [θ]: by sympathising with Fëanor; or by being one fo the speakers who never switched to [s] in the first place (e.g. the House of Finarfin, or the Vanyar etc.); or by being one of the loremasters who preferred þ.
[Important note: not all words with s in Quenya are related to the s vs. þ issue! Some words indeed simply have a s in them.]
