Without digging deep to double-check if it will do everything you list above, we can heavily recommend Ulead VideoStudio. We run multiple copies of v10 Plus (which, incidentally, is still one of the few which is 'Core 2 Duo' aware' and which speeds up transcoding etc by a further 30% or so.)
All reports we've had of the current 11 Plus are very positive.
As it's well within your budget, we suggest the 'box' version as the printed user-guide is excellent.
We'll be glad to dig deeper if you need more info. HTH.