Will the stock Intel Heat Sink be sufficient?

If you don't overclock then the stock cooler will work fine. The thermal paste is also fine on the stock cooler.

If you're going with a build with a 770, why not get an aftermarket cooler, much better temperatures. Although, it depends if you're going to be playing with it a lot or if you're just going to game now and then. If you're going to be gaming a lot, just buy an aftermarket cooler, I use a corsair h60, it's only 60 bucks and it's a closed loop water cooler, keeps temperatures nice and low, where they should be. The stock cooler really isn't that good, but I guess you could use it if you really needed to

It will be fine, but it will get a bit loud. Honestly, I don't like how it gets really noisy when you start playing games and stuff that puts the CPU on load, but you might be fine with it. Personally, on all the computers I build, I always put atleast a Hyper 212 Evo on there which will help it run cooler and is significantly quieter.

At stock speeds you'll be fine unless you are attempting to squeeze everything in to a very small, low profile case or want a super quiet machine (in which cases there are far greater sources of noise to consider first). Intel's stock HSF is both effective and reliable: remember that Intel have a vested interest in providing a decent heatsink since if it cooks your processor that is a potential warranty claim for them. The third party suppliers have no such come back.

In any event a lot of third party heatsinks are frankly poorly designed from a technical viewpoint and designed more to appeal to the buyer's sense of aesthetics. Any shiny polished contraptions you see have fallen victim to this tendency - it doesn't matter how impressive they LOOK, simple physics is that a dark matt finish is a much more effective radiator.