A bad case either does not cool, or it cools at obnoxious volumes. A good case cools at good volumes.
I have a Corsair 300R and 500R and have used other cases. I can't really recommend the 500R at its price level. The fan controller is of limited use (use a mobo or dedicated fan controller like a NZXT Sentry Mesh), the build quality is mostly okay but the spring on one of the 5.25" bays popped out and it's almost impossible to put back in, and one of my USB3 ports disintegrated when I pulled a device out. Corsair customer service is a little slow but once they respond a couple of days later, they are very fast and good, so long as you're in warranty.
A Corsair 300R is a little too cheap imho, in that it doesn't even have mesh 5.25" bay covers or anything, just solid plastic. If they would at least drill holes into it, I could tape some dryer sheets to filter it myself, but nope, just solid plastic.
A Corsair 400R then, may be the best compromise in that series. The base fans should be adequate, and you can further dampen noise by getting rubber fan mounts and quieter fans that still offer some kick. You can also use AC filters or dryer sheets to paper over the huge holes that Corsair leaves in its side panels (can you say dust problem?!).
One thing common to all Corsair cases is how thick they are. That is important to fit 160mm tower coolers like 212/212EVOs and still have space left over for internally mounted side fans, AND have some decent space behind the motherboard to stash cables.
Antec is okay but suffers the same high-price problem Corsair suffers from.
If you want good but cheap, try getting a last-generation USB 2.0 case that is being discontinued just because it lacks USB 3.0 front ports, on sale for cheap. If you absolutely need front access to USB 3.0 ports, get a USB3 hub or extension cord to get access to the rear ports; or get a USB3 adapter to fit in your 3.5 or 5.25" bay if you have one.
Also know that unless you are watercooling or something, don't bother using the top fan mounts. Bottom fan mount, maybe.. if only to feed a power-hungry GPU or something. But top doesn't do much and can actually mess up your airflow. You'd be better off erecting a vertically mounted 120mm fan in your top three 5.25" bays (use foam packing material, tap, zip ties, whatever... and filter it!).
My favorite case ever: the CM Storm Sniper Black. Huge, quiet, sturdy, tons of bays, never broke on me, and the only reason I switched was because it didn't have native USB3 and I wanted to free up a bay that was occupied by a USB3-to-3.5" adapter. Stupid move on my part. Love that case, see if you can get it on sale for under $100 and add your own USB3 front ports via adapter if it matters that much to you (or a hub or extension cord).