Either can be useful. While a cordless blender lets you carry it anywhere you choose, it may run out of power in the middle of blending. That can be a big inconvenience.
Yes, blade quality is very important. The blades on a good hand blender must be made of food-grade material. Metal or stainless steel blades, to be accurate, or the best option since they’re durable, rust-free, and long-lasting.