Best Editing Software for my needs?

I hope someone can advise me.

I have been using Pinnacle Studio 12 to make some home videos. It's been fairly simple to use up to now. However I am trying a more ambitious project and I think I might need a more advanced editing program. The project involves a virtual news set - I am filming a presenter against a green screen which I am then going to layer over the virtual news background using chromakey. This could be done on Pinnacle Studio 12, but the virtual studio background also has a seperate 'blank' TV screen within it that I could also use with chromakey. I basically want to be able to utilise 3 tracks of video at the same time - ie the virtual set background, the presenter against the green screen superimposed on the background, and the 'TV screen' within the virtual background to be showing clips that the presenter is referring to (which could also be enlarged to fullscreen and back down again).

Does anyone know what the most suitable software would be for me to be able to acheive this? Any help would be greatly appreciated.