DA20 pilot reported they lost control of the aircraft while landing in a strong crosswind resulting in a runway excursion causing the nose wheel to break off and a prop strike.

Narrative

I departed the ZZZ for ZZZ1 to satisfy the requirements of the solo cross country for my private pilot add on rating. I received VFR flight following for both legs of the flight and made successful landings at ZZZ1 and ZZZ2 airports before returning back to ZZZ. I was handed off to the ZZZ Tower approximately 6 miles east of the airfield and cleared to land via an extended left base for XXR. Approximately 2 miles east Tower advised me that the winds had shifted to 190 at 10G19 kts and asked if I would like to land a different runway. I figured I would be accepting a crosswind regardless of which runway I chose so rather than taking a straight in for Runway YY which was an unfamiliar runway to me; I chose the familiar sight picture of base to final to Runway XXR. On final approach I set my approach speed at 60 kts; deployed my landing flaps; verified that the wind sock showed a right cross wind; and set my flight controls to stay aligned with the runway (left rudder; right aileron). The descent felt normal so I continued the approach. Upon touchdown I felt a wind gust lift me a foot or two back off the runway. I decided to let the aircraft settle back onto the runway when a second bigger gust lifted me back up and pushed me toward the left side of the runway. At this point I introduced full throttle and right rudder but was unable to arrest the descent before porpoising back to the ground. I then porpoised off the left side of the runway into the gravel causing the nose wheel to break off followed by a subsequent propeller strike. I then slid to a stop at which point notified Tower of my position and situation while I pulled the fuel shut off valve; put the mixture to idle cutoff; and turned off all electrical switches. When I egressed the plane I felt a significant gust from a right quartering tail wind presumably outflow winds from a storm atop ZZZ3 to the west. As pilots and professionals in our field it is our job to understand and to mitigate risks to the best of our abilities. We gain experience from situations that we are lucky enough to walk away from and from the experiences of our friends who were not so lucky. In my case I opted to use a familiar runway with a 70 degree right crosswind rather than a short unfamiliar runway with a 60 degree left crosswind but hindsight says there was a thunderstorm 20 miles away in the westerly direction perhaps it would have been prudent to keep the plane facing the storm.