Well I don't think there is a "best" case that meets your criteria, but I suggest the Antec SX830.
-It's available at several online retailers at a reasonable price
-I imagine it can be quiet with the right fans (4 80mm snap-ons but you don't have to use them all)
-excellent cooling (so I hear)
-Not screwless unfortunately, but it does utilize a 'door handle' to remove one of the side panels once the back screws are removed.
-300 Watt psu
Anyway take a look:
Antec SX830
If you don't mind the somewhat large size, it's a nice case. My friend has the Antec KS282. It's a smaller, value case from Antec with the same psu. It's
ok. The side doors are a very tight fit and hard to slide off. I also cut myself on a sharp edge, I was definitely not happy about that. I think the SX830 being a higher class case than the KS282, will have a better finish and quality. Again, it is on the large side (between a mid-tower and a tower).
I was also going to suggest Palo Alto (case used for Dell/Micron machines last time I checked) cases, but those are difficult to buy and I don't think they have a mid-tower with 3-5 1/4" drive bays. You might have better luck asking around in the Case and Cooling forum.
Al
But for the $120 the Antec is selling for right now, it's pretty hard to beat.
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