but the G3220 has a graphic chip less powerfull than i3.
due to noise: i don't want to listen no noise!
Yes, Pentium/Celeron have a less powerful IGP: it's a trade off, those CPU cost the half or less of a Core i3, something has been stripped down.
The question is: do you have any task for those extra unified shaders? If you have some specific need, then a Core i3 may worth: otherwise, YMMV.
The nominal TDP is not a relevant issue: any modern Intel CPU (Sandy/Ivy/Haswell) may draw about the same power, providing they are conveniently either undervolted or underclocked (so which motherboard is the real issue, IMO).
The proposed setup would combine about the smallest size with the extreme quietness: due to law of physics, it's extremely difficult to achieve such a goal, while retaining a normal CPU power. Particularly if you take into account that such a small enclosure would be more probably that not very close to the operator ears (so any moving part - fan, hdd - can be more easily audible).
If you add further requirements (i.e. the enclosure cost, those front USB 3 ports, and so on), then I'm afraid your purpose cannot be fulfilled.
Eventually, a 35W Haswell (or an undervolted 53W SKU) cannot be cooled safely with any passive heatsink in such a small enclosure without any case fans, period: I guess you should change either the proposed enclosure, or the CPU TDP (not to mention that you should cure very carefully the relevant placement).