I read the review on the site for the SG09 which has the same build as the SG10, it was said that the fans are a bit noisy which is why I'm thinking of replacing the rear cooler with the Noctua NF-S12A ULN and not using the side cooler which is meant for the GPU (as I'm not using one).
Will the system be silent? I plan on running the top system fan on the low setting to reduce noise further.
No, it won't be silent, IMHO the proposed setup can't be silent.
First of all, the baseline noise of the SG09/10 is about 20dB: still a quiet level in the SPCR scale, but undoubtely a fairly high one, so if you were relatively near to your rig, or there were a straight path from it to your ears, that system would be easy noticeable (even if not obtrusive).
Then the major noise source will be the top fan, not the rear one (which is actually far quieter and sports a similar noise signature): as you may check at the end of this page
even if dialed down with the fan controller to the Low level, it's still too much loud. You may try to swap it, but then you will loose its cooling prowess.
Or you may try to dial it down (or undervolting) furtherly, and that Gigabyte motherboard could not be up to the task.
Anyway when dialed down it would be quieter, but IMHO the system would be still not suitable for a close to operator placement, when your expectations were about a "silent rig" (I had similar fans in my previous Raven case).
Even the other two fans aren't blameless: so you may find either convenient to swap it with something with a more benign sound signature and an overall low noise (no need for expensive Noctuas, either Scythes or Nexus would work flawlessly), or to remove altogether.
As said, usually fan control on Gigabyte boards is pretty poor: so, unless you have other reasons to choose those Gigabyte boards, noise wise I wouldn't recommend them.
Perhaps something like an ASRock H87M Pro 4 could work better in this respect, but I don't know whether it can handle three case fans or not (check the online manuals): usually mATX motherboards with more than two controllable fan headers are premium/gaming ones, usually very expensive, but you can't rely on Silverstone own fan controller if you aim to "silence", so the only alternative could be a programmable external fan controller (which definitely is not the easiest way).
As you have an IGP rig, you may also think to use a full PWM setup with an active splitter on the CPU header of a not-premium/gaming mobo (but you do need two-three replacement PWM case fans).
Than there's the PSU question: definitely there's no reason to have a fanless (and expensive) PSU within a system which at first glance sports four fans (and two relatively loud ones too).
At any rate, if you have a supplier which will swap it at first request (last batches would seem a tad prone to coil whining, but YMMV), it's still a good choice: superb performance and reliability.
Otherwise IMVHO something like a BeQuiet! E-9 480CM could be preferable: not as good as an X-series, but almost inaudible in an IGP rig and probably a safer bet, noise-wise. Whether you may like a semi-fanless operation, even a Corsair RM-series could be a good choice.
About parts picking, I'd advice to go with a dual channel kit, instead of the single channel 1 x 4Gb stick: on Intel architecture the bandwidth gain is fairly more noticeable than on AMD platforms, and there should be no price-penalty. I have some doubt also on the Vertex 4 choice (as it's not the fastest kid in town, and reliability-wise OCZ has not a track proven record), but that choice is up to you.
Eventually I don't understand the choice to go with the NH-L12 cooler: undoubtedly it is a very good and quiet heatsink but, giving the ample space inside the G10, you won't exploit its distinctive advantage. P.S.:
to be fair, there would be one configuration which could be near silent, using the proposed parts: providing you won't use any of the SG10 stock case fan (and providing the X-400 won't squeal). Temperature-wise, YMMV: even if it can be useful, you should not need that side fan in an IGP rig but, particularly with a fanless PSU, you may need at least an exhaust, even with a fifty watter like the i3, and so to swap the rear fan with a quieter, more benignly sounding one. Please take note that in this latter case the proposed Gigabyte mobo could not be up to the task.