Although a single outlet will likely work for your set up, it's always better if you can distribute the load between at least two outlets. They don't necessarily need to be dedicated, especially if you are using two that are on different circuit breakers. This will give you some redundancy especially when using a GFCI device, which is quite sensitive. If you're not home when a breaker or GFCI trips, running on two separate circuits may just save the bacon... err fish.
A single 15 amp circuit can handle a maximum of 1800 watts, but that's not continuously. 1500 watts is a better number safety wise if you're going to calculate your load on a 15 amp breaker. Keep in mind that if you use an existing outlet, other devices will occasionally affect this circuit. A worthwhile investment of about $12 will get you the "Electrical Code Simplified" (residential) published by PS Knight. Should be available at most Home Reno outlets. This will provide you with a wealth of understandable info on wiring requirements.
Hold on, just checked my edition and they have a website:
http://www.psknight.com/