I'm a certified storm spotter (NOT a storm chaser!). A storm spotter "protects" where they live for the most part. We don't go around the country chasing storms.
My weather apps I need and can't live without;
RadarScope (with in-app purchase)
WeatherPro (with in-app purchase)
Weather Bug
MeteoEarth
Let me explain why these are my go to favorite weather apps
RadarScope give almost realtime radar data, when severe weather is in the radars range, the NWS puts the radar into SAIL mode which updates the radar frames ever 2-3 mins. So the radar data is never older and 3 mins during storms. When no storms are in the area, SAIL mode is disabled and the radar frames are 5-6 mins old. App support is excellent!
WeatherPro uses USA and European data and hashes out the forecast for any given area in the world. Over time, I find myself using WeatherPro because it's seems more accurate for forecasts due to them using USA and European global weather data.
WeatherBug is great for instant hyper local real time weather data like winds and temp, humidity, etc. There are 6 sensors at the schools within 5 miles of my location
MeteoEarth has the best future graphics and is from the same people who make WeatherPro, so it's in-app purchase can be used in 3 of their apps. Pay once for a years worth of data and use it in 3 apps at no additional charge.