First things first... WELCOME to the forum!
As to your question the amount of water needed is going to depend on a couple of factors.
1. What size are you classifying your materials to? The larger the materials, the more water you're going to need to move them through the sluice.
2. What kind of angle do you set it up at? This is a balancing act and the more angle the less water is needed BUT the more chances you have of blowing gold out the end of the sluice and into the tailings. Too little water flow and your riffles are going to load up. The perfect setup should have the riffles clearing excess materials out in about 5-7 seconds.
On my highbanker I keep it set at about 4-1/2 degrees downward angle and run 2000 gph through it. While digging I classify to 1/2 inch but my headerbox screens it down to 1/4 inch as I load it into the system. At this flow and size it does a pretty good job of holding onto the fines as well as the nuggets and flakes. I rarely have any vlaues travel more than 1/3 of the way down the sluice.
As to pumps, it's always best to get the largest one you can afford. If it provides too much flow then you can add a valve to cut the flow down some. Always figure your water needs from the widest point of your sluice. In your case 14 inches. Saying that, you should be able to use a 3000 GPH pump and have a little more flow than you need. Because of this you can either lessen the angle of the box a little bit or add a valve to cut back onthe water.
Hope this helps
GI