First of all, I see that you are growing in planters. While I think this is okay for the first year, think about the quality of the soil in there in subsequent years. If you do not feed them a LOT of nitrogen, the soil will quickly be depleted and you may very soon want to think about planting them in the ground so that they can establish more permanent roots (rhizomes) and generally grow bigger and better. Any time that the rhizomes are disturbed or the soil is replaced, the vigor of the plant tends to start all over again. Don't expect a good crop in any year where the rhizomes are disturbed. This includes this year if you have just planted them. They will produce a lot of hops in the 2nd year after planting and every year after if you don't move the rhizomes or soil.
Now to answer your question. I have been growing hops for almost 15 years now. For several years I have been allowing 6 bines per plant. This means that each spring I have to remove several dozen of the baby bines per plant, they seem to produce around 50 bines each if allowed and that would be bad indeed. However, the total weight harvested at 6 bines per plant per year has been falling for a few years now here, and I keep telling myself that 6 is just too much. So this year I am pruning them all out except for just 4 bines per plant. Actually I keep 5 or 6 in the early spring, like right now, because often 1 or 2 of them will break off by bumping into them or while training them onto the strings, and when this occurs then I'll still have a spare ready to go. But by about mid-May when they begin climbing 2-3 feet high, then it's time to limit them to just about 4 per plant, in my experience. There is too much competition when there are too many. And the taller they can grow (or longer, if along a lower fence-line), the more they seem to produce. The majority of your hops will be at the very top of the plant, with relatively very few down lower. Too many bines will prevent them from growing tall enough to produce at their optimum, in my experience.
So that is my recommendation. As I said, I have been growing hops for almost 15 years. They come back strong as ever, every year. They continue to spread farther and farther out from the main plant, if I allowed it. Otherwise they would have taken over a large portion of my yard. So I have to pull a few of the rhizomes out of the ground every year at the perimeter to keep the hops growing where I want them to be, and not where I don't. Containers of course would limit this spread, but at what cost to the long term well being of the plant if the soil quality is depleted over time?
Hops are fun and easy to grow. I use mine for bittering mostly, but the aroma is also wonderful when fresh. I find the alpha acid content to be very reliable here, about mid to upper range for whichever variety is grown.