Optional signup with the big three (Facebook, Google+, and create-your-own-email).

As for the limited feature set before choosing one of those three, I used to think that was necessary, but I've noticed more and more people don't care as long as they can choose one of the big three. Especially on mobile where typing passwords, etc, is difficult. It is much easier just to click the Facebook or Google buttons.

It depends on what you build. Generally you should require signin for things that need signin - requiring them for things that don't will drive users away. You can still uniquely identify users if you need to, and then convert them to an actual account if/when they signup.

That's pretty much what I was thinking. The discovery part of the app would be open but the profile based things would of course need a login.

What ways can you uniquely identify users who aren't logged in?

browsers are surprisingly unique to each user; see "browser fingerprinting" https://panopticlick.eff.org/

You could also just use cookies, which is perhaps a more socially conscious way of handing it.

Browser fingerprinting fails for cases where a computer is shared. That includes both home and public terminals. Not to mention it creeps people out and lacks any type of security.