According to Newegg, the i7 3770 lists for $300, the i7 3770S for $305. So, not much of a price difference, and if you aren't comfortable with underclocking, the S version might be the better choice.
In my newest (last year's) build, I chose an i5 2400S and am happy with it. I'm not sure I would do it again, though, as the "less isn't necessarily more" arguments forwarded here at SPCR make sense if you want to keep the overclocking option.
Many quiet PC builders regularly select S or T models, see http://www.endpcnoise.com
(the latter's in German, but the specs don't need translation). They must have their reasons.
As for HD4000, that I would prefer, too, though if you just want to look at video clips or a DVD now and then, HD2500 is adequate.
The more important question is whether i5 or i7. If you are doing some hefty number crunching, i7 is the better choice. If not, you'll be paying a premium for a speed boost that in many applications wouldn't be that noticeable or noticeable at all. I have been considering an i7 myself because I use Dragon Naturally Speaking and (SPCR mavens correct me, please) the i7 makes a perceptible difference when using that program.
For many, all roads lead to the i5 3570K, which has HD4000, can be underclocked, and is reasonably priced.
The i5 3475S is an -S processor and has HD4000, but I can't find it listed for sale.
Regarding a heatsink, I have seen the HR-02 used passively in the Temjin case and that might be a good silencing option with a 65W CPU.
Thanks, RHN (and others). for the i5/i7 info, and for the HR-02 suggestion.
For me, the attraction of the i7-3770S is that Intel has figured out (and presumably carefully tested) whatever they did to get it to 65W TDP), an exercise that I'm not likely to do as well -- and I don't intend to overclock later on.
Even so, underclocking an i5-3570K is an interesting option, and I have these questions/concerns:
1. Is a Z77 board needed to underclock? (if so, the extra cost cancels part of the i5 savings). The Gigabyte GA-H77M-D3H board has some clocking options, but I don't know if they're sufficient.
2. Is there an unambiguous underclocking path to 65W TDP that is stable (and equivalent to, say, the i5-3475S)? (I've seen so many clocking opinions/problems that it's not clear the cost savings is worth it, especially since both the i5 and i7 have more power than I need. My goal is stable 65 TDP operation, not maximized 65 TDP performance.)