Welcome to SPCR... forever?
For non-gamers who don't do heavy graphics or video editing, an integrated motherboard is perfect. I am constantly on the lookout for good boards with built-in VGA for friends/assoc. who want quiet PCs. They're great for quiet computing. Built-in VGA is usually found only on mATX boards that tend to be less full featured, being geared towards commercial system integrators. This often means fewer features in BIOS, particularly. The most impt feature being Vcore under
voltability and underclockability for a cooler running CPU.
There are some gems if you look hard. But a low end graphics card is a fine option, too; not much heat and no fan.
In the A64, there are very few on-board VGA mobos right now, and they're all mATX. MSI has one, so does ECS, Gigabyte. There are probably others.
Regarding a case -- it's not really how much you spend, the expensive cases are so more because of cosmetics than superior functionality but a case is VERY
important. Airflow is everything: Quiet computing's basic mantra goes something like this:
1. Choose the sturdiest case with the most unrestricted airflow potential so that you can get the quietest fans and run them super slow yet have good airflow
2. Choose the coolest components that will give you the computing power you need.
3. Choose the best heatsinks so you can run super quiet fans on them at min speed
4. Choose the quietest PSU & drives.
Read the Recommended Cases article
-- in fact, read the the whole recommended section! http://www.silentpcreview.com/section10.html