For my ETSS skimmer I'm using an equivalent pan-world pump. Once I finish setting up my 360g display I'll have my sump / equipment room in my basement with the tank on the main floor. I'll be using a Dolphin Ampmaster ES5500 pump, which is 5500 gph at 5' head (roughly 6500 gph at 0') used as a return. I'll probably split this return to run my downdraft skimmer depending on if I re-use my ETSS on the new system or not.
Perhaps post a picture of your beckett skimmer, and someone might be able to identify it? There aren't too many commercial manufacturers of the becketts to pick from, but it might be a DIY job or a small scale shop who built it. I would guess that a 1200gph pressure pump would be the bare minimum to run a moderate sized beckett skimmer for something like a 150g system since the becketts have so much more back-pressure on the pump than even an equivalent downdraft style skimmer (like the ETSS). While I can use a 1200gph pressure pump on my downdraft skimmer to handle a 300g tank, I doubt the same pump would run a beckett skimmer sized for the same system.