For a patient with 1.25D of with-the-rule astigmatism, who is active outdoors and who operates heavy construction equipment, the most appropriate type of contact lens would be:

For a patient with 1.25D of with-the-rule astigmatism who is active outdoors and operates heavy construction equipment, soft toric lenses are the most appropriate choice. This is because soft toric lenses are specifically designed to correct astigmatism by providing a different curvature in one meridian compared to another. They ensure that the lens aligns correctly on the eye, which is crucial for maintaining clear vision in individuals with astigmatism.

In this case, the patient's outdoor activities and the operation of heavy machinery place a premium on visual stability and comfort. Soft toric lenses offer a combination of comfort and visual acuity, accommodating the patient's astigmatism effectively while being durable enough to handle an active lifestyle.

These lenses also tend to be easier to insert and remove, which can be beneficial for someone frequently engaging in outdoor activities. Additionally, soft toric lenses often come with UV protection, an important feature for outdoor exposure.

Given these considerations, soft toric lenses stand out as the best option for addressing both the refractive needs and the lifestyle demands of the patient.