When would be the best time to chase tornadoes?

I am going to make an incredible living in my adult hood. I am going to go to college for Flash Game development, and I will also go to college so that I can chase tornadoes(maybe I don't need college for tornado chasing, but let's just say I will have to just in case). I don't want to move to tornado alley permanently. Because then in the town I would live in, if it get's hit by a tornado, will be level'd(along with my house) then I will never be able to publish any flash games. I will keep my hometown in New York where I live now. Then, when the most active parts of tornado season arrive, I move down to tornado alley temporarily, so that I can capture videos of tornadoes. Then, when the most active parts of tornado season is over, I move back home to continue my other life until the next tornado season. And then I move back to tornado alley to live that life again and then move back again... again. So, I was going to make a life schedule. Can somebody tell me which seasons are the most active parts of tornado season? That would help me out a lot. Thanks a million.