For a construction site, you need a trash bin that's tough, simple to use, and easy to move around. I'd skip anything fancy. My top recommendation is a basic steel rolling dumpster. It's essentially a heavy-duty metal bin on wheels. They're almost indestructible, can handle heavy debris and weather, and the wheels make it easy to roll to the pickup point. No lids or complicated parts to break.
A great alternative is a large, high-density polyethylene (poly) cart. Look for a contractor-grade model with reinforced walls and heavy-duty wheels. They're lighter than steel, resist rust and chemicals, and are still very durable for daily site use. The key is to avoid residential-style bins. You want something with thick walls, robust axles, and a simple, open-top design for quick tossing of waste materials. Keep it simple, heavy-duty, and mobile.