Roping is a central skill for cowboys. Although there are times when herding cows into pens and then into narrow alleys and then into squeeze chutes where they can be stopped and held for inspection, doctoring and branding is advantageous, the experience of most cowboys is that roping is still the best and least harmful way to capture a cow and take it to ground where it can be handled. And it’s the only way if you’re in open country.
Most cowboys in the US today use nylon or polyester ropes from 30-60 feet long depending on the type of work they are doing. Team roping competition (two cowboys try to rope a calf in the least time) usually uses a shorter rope because they are close to the calf to reduce travel time. And in a small pen situation a 35 foot rope is appropriate (the shorter the rope the less chance of loops getting tangled). In real ranch roping longer 50-60 foot length are common because the closer you get to a cow in the open the more likely it is to move away. But it takes a strong arm to throw 60 feet!
There are many excellent rope manufacturers but I personally like Cactus Ropes.