Cut down what makes sense and plant what you want. Mother nature is going to provide you with more of the same so to speak. If you cut basswood, ash, cherry and maple.....what is going to come back on it's own will be the very same....plus potentially any invasive plants that you now exposed to sunlight. If you want certain shrubs of trees in that area.....be prepared to plant and give them a fighting chance. I would look real close for ANY oak saplings come spring. You certainly want to release those. I would think you have at least a few hiding from you in there somewhere. Mark them with flagging tape. I had a guy once tel me he had a part of his place that didn't have any oaks on it. I visited the property and he had far more oaks in that are than he thought! They where just smaller and a different type than he had identified on other areas of the property. Make sure you have any invasives and or difficult to control species under control before you cut. IF you have jap bush honeysuckle or Multi-floral rose or the like they can become VERY difficult to control once you release them to the sunlight thru logging.