- cooler: The Gelid Tranquilo is quiet..don't know about the Shero. The 212 Evo is known to be pretty quiet.
- gfx card: I didn't do a deep dive. However, Asus in general makes quiet gfx cards. Adding this card will be noisier than using the integrated graphics, but then again, either you need the fps or you don't.
I would just to point out that the Gelid Slim Hero is a sub-par cooler, it could be a viable choice just for cramped space, while I won't bet that specific ASUS card were enough quiet, and for that price it is a tad difficult to find something which is quiet and fast at the same time (the cheapest option could be the Sapphire Ultimate 7750, about 20 USD more from TigerDirect after MIR, while fanned relatively quiet cards goes for at least 130-150 USD).
Last but not least, about the proposed partpicker setup, maybe an Intel G3420 should be a better pick than the G3430 (-20% in price, about the same performance).