Any green bean recommendation is personal preference. They all have something to recommend them. My wife insists I raise Blue Lake as she says they smell more like green beans than the others I've tried. I'd suggest trying different ones in different years until you find one that stands out for you.
I have not tried the purple beans but I understand at least some varieties of them cook up green.
I understand some of the frustration with weeds in carrots. I usually only weed them once after they come up, then they shade out enough of the new the weeds that try to sprout. I usually wind up watering my carrots a couple of times when it is dry to help them come up so I often have a crust when it is time to weed them. I wait until it is a little damp to weed them. I do less damage to the growing carrots that way. And I usually gently water them after I weed to settle them back down.
One way that might work to help keep the number of weeds down would be to prepare the ground to sow the carrot seeds about three weeks in advance, then cover it with black plastic. This should sprout and kill most of the weed seeds right at the surface. Then, when you plant the carrots, disturb the ground as little as possible to not bring more weed seeds to the sprouting region. Carrot seeds are so fine they don't have to be buried very deeply so you can do this without disturbing the soil much. It would not help on seeds that need more cover to germinate.
I got my first good carrot yesterday, by the way.
Good luck!
I love the yellow ones just for interesting color. My favorite green bean is Slenderette. It holds the beans for SO long without getting overripe and each plant is loaded!
