Generally you want to look for a supply that has the rated wattage on it's 12v line somewhere near it's total rated capacity. For instance, When I google Silverstone 500W you get this image:
http://images.anandtech.com/doci/4908/17_leistung.jpg
Notice how it's a 500watt supply and the 12v line supplies 34 amps, so 12 * 34 = 408 watts. Not too bad, but not great either.
The original supply you linked has 2 12v rails, 19A each, so 19 * 12 = 228 watts for each rail, but it has a note right on it that the total of the two can't exceed 368 watts... 368 for a 650 watt advertised supply? Terrible.
Something like a Corsair CX 500 found here:
http://www.newegg.ca/Product/Product.aspx?Item=N82E16817139027 . . . 38 amps for a 500 watt supply, so 12 * 38 = 456 watts... much better.
It doesn't always work out that you get a quality supply that way, but since computers these days get a vast majority of their power from the 12v lines (it didn't used to be that way, which is why some are designed differently) it will really help when shopping around. Do you have to buy it from a specific store or something, is that why you only have a few models to choose from?
As a personal preference I usually like to stick to single rail designs so there are no issues with using adapters in weird scenarios later, but that's more of a preference than a requirement.
The LC600H-12 you mentioned is 480 for a 600 watt supply, while it would probably run your machine just fine take note that the CX500 I mentioned above can supply 456 and is rated at 500 watts and this one only 480 for 600 watts? It sounds like they are trying to over sell what their supply can actually do from the overall capacity rating, which I think is usually a bad sign for the overall quality of the product.