For both gaming, typing, and backlit? You're looking at, in increasing price order, a Rosewill backlit mechanical keyboard, a Cooler Master Quick Fire Pro (possibly the TK version), a Corsair Vengeance K90, or, at the highest end of your budget, a Ducky Shine II.
Look for MX Brown or MX Red mechanical keys: they are typically considered the best for gaming (lighter activation, no loud clicking), though MX Black is okay (harder activation, but linear and non-clicky).
When I say activation, I mean how difficult the key is to press--MX Brown and Red are roughly as difficult to push as a full sized, non-chiclet keyboard. MX Black is a little harder, but most won't notice too much (or they'll easily adjust). "Linear" means that the keys' resistance is identical throughout pushing the key down (some variants, like MX Blue, Green, and Clear have an a point where the key "gives" before the key actually bottoms out, telling you when the key actually activates as opposed to merely hitting the bottom). And lound/clicky means what it sounds like: some of these key types (blue, green, clear) make a loud click when they activate (louder than the norm).
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