I don't think any historian today knows, and I don't think the historical community of today will even make the decision. In my view, the decision will be made by archivists who have surprisingly little interest in anticipating the needs and future research interests of historians.

As of roughly the WW2 era, entities like the US government have produced far, far more records than people could hope to process effectively. Sure, much of that were redundant records (you don't need to keep 20 copies of the same document, right?) but a lot of it also wasn't. Since about that time, perhaps 5% of what was produced has been saved for future reference. First off, that's a minuscule amount. Second, that proportion has only gotten worse over time, as you can imagined how expansions in government and technology have multiplied the amount of records created (especially vs. the funds invested in archiving, which to put it delicately, haven't kept up).

So who makes the decisions about what's kept and what isn't? Archivists, that's who. There was a time when they were deeply interested in what questions historians asked, and what governed their research questions and methods. That time ended roughly in the 50's. Why? Because historians began radically changing the way they conducted their craft, and rightly so. They underwent the social and later the cultural turn, both of which significantly altered the types of questions they asked and the types of sources they used to answer them. To put it mildly, those changes promised to send recordkeeping off the rails because it became incredibly difficult to figure out what was important and what wasn't. The sheer volume made simply "keeping everything" impossible, and when historians moved in a direction which made discerning important documents from unnecessary ones impossible, archivists took it upon themselves. They became concerned with organizational integrity, provenance, and original order as governing principles, and that is not by any means a criticism. They were tasked with the impossible and performed an act of triage.

I expect the same thing will happen with the internet. It's too much. The task of combing through the internet for every scrap of information associated with, say, the 2016 election, would be impossible for the 2116 historians (barring, perhaps, technology I can't conceive of). I highly doubt most of the information will even be retained that long. If it isn't, the task of discerning what's kept and what isn't will be decided at best by digital archivists and at worst by the corporate stewards of the various platforms on which this information was shared (Wordpress, Twitter, Facebook, etc), who will likely base their decisions on records management compliance standards (most likely legal requirements, if there are any), or things like server capacity. At best, if the decisions rest wholly in the hands of archivists, those people won't care one bit about the hypothetical research interests of historians not yet born.

The fact of the matter is, the internet will constitute a nearly unfathomable glut of information for future historians, who will either be forced to cull useful information from the deluge through yet-undetermined means or else examined previously curated information--this curated information will either be extremely sparse due to the limited means of archivists (unless they are blessed with increased financial and human support) or else be a small recorded fraction of what exists today, selected by non historians using yet-unknown criteria which may or may not have any historical interest in mind.

This is a major reason why historians shy away from claiming they can uncover the 'truth' of the past. In addition to acknowledging the inherent subjectivity of themselves and the creators of historical sources, there's the undeniable fact that the vast majority of the historical record simply has not survived. Some, probably most of it (like the day-to-day thoughts/experiences of anyone who doesn't keep a diary) was never recorded at all, some of the recorded stuff simply didn't survive (everything from overzealous spring cleaning to the burning of the Library of Alexandria), and some of it was selected to be discarded by the recordkeepers for one reason or another. I for one think it's unfortunate how unaware historians are of the gap between theirs and archival professions. They're quick to problematize the archive yet reluctant to fully understand what they're problematizing.

If you want to read up on the divergence of the archival and historical professions, and more about how the historical record is compiled by archivists, check out Blouin and Rosenberg's Processing the Past. It's excellent.