A top class desktop PC case costs no more than $150 or so, while the cheapest cases are around $50. I think that extra $100 (or less) is the best place to invest in a computer, never mind the looks. You can get a really quiet powersource, dustproof chassis (only air intake is through a reusable air filter and the closed chassis is slightly overpressurized; this also helps make the machine more silent), 120mm fan(s), sturdy construction, possibly thumb screws, stuff like that. Then some case mods. I'd use some zip ties to round the power cords and make the airflow better ($1), then I'd tack some heavy automotive rubber carpet on the insides of the case to damp vibration (<$10). If I knew a cheap, no-fuss way to isolate hard drive vibration from the case, I'd do that as well.
Oh, and when you get a good case, the price is divided between multiple computers - chances are, the case will far outlast any single computer.