A silent psu (aka fanless) are silly expensive - got one myself, so stick with a quiet one - used the enermax and Zalman below personally - and the corsair is well respected.
The Enermax 82+pro 385w (not available at OcUK) Corsair VX 450W, or the Zalman ZM500-HP
Case - almost every case can be made quiet with the right hardware and simple mods.
steel cases make good silent pc's or high end aluminum ones if you have the budget.
Aim for a very simple airflow path with no 'pocket' if possable.
Block vents that might shortcut airpaths (rear vents when just using a psu fan are the most obvious)
HHD - SDD are not really in budget so bungee mod your Seagate (usually enought, but an encloure also helps - silentmaxx/GPU/Mcubed especially is using only psu fan)
CPU - low voltage duel core - E5200 is a great little chip - even oc'ed it runs nice and cool at around 1v
Cooling - Thermalright HR-01plus, Scythe ninja or go the whole hog and get a secondhand Zalman Reserator (1v2 1plus or 2)
Mobo - Gigabyte GA-EP43-DS3 (b-grade) or the asus above. You'll need to swap the nb heatsink to Zalman ZM-NBF47, Noctua NC-U6 or thermalright HR-05 if just using the PSU fan - if you include a single case fan at 7v (or 5v) then only get one of these if oc'ing
Fan - one 120mm at 7v or lower. (not up to speed on what's best as i don't use them anymore)
Leads - cable tidying is a must with low airflow cases
visit SPCR - silentpcreview.com for loads of extra reading