You should get an ssd. They don't have any mechanical moving parts, so they don't make any sound. They also produce less heat which allows you to turn down the speed of your casefans. The OCZ Agility is affordable and very fast. You could get a dampening enclosure for your hard disk and a dampening kit for your case, but even then you'll probably still hear your hdd. So it's better to just get an ssd. I also suggest getting fanless graphic cards, a passive cpu cooler and low rpm casefans. I have 2 MSI Radeon 4350 cards, both passively cooled. I have the Scythe Ninja 2 cpu cooler in fanless mode. And I have 2 120mm Scythe Gentle Typhoons spinning at 500rpm.
Water cooling baby, water cooling. Overclock that puppy if desired. Buy good fans yes, but a couple 120 fans at 500 RMP will do a good job of sucking in some dust but not cool anything. You have to be realistic about cooling and not let quiet overtake the main mission. Watercooling is the best way to cool for the money. Less noise is how good you plan and build the box.
A trading computer doesn't need a lot of cooling. It's not a gaming rig. The Scythe GT fans that I have displace 31 m³/h at only 5 dbA. Most fans will need around 10 dbA to displace the same amount of air.
if your feeling industrious you could place the drive cage atop a sheet of latex rubber and attach the drives to it through silicone gromets, then you'll have silence.