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With respect to your question, that's something that can easily be done with iMovie on a Mac.
iMovie for the iPad is available as an app from the iTunes store. I haven't used it so I can't speak to what it can and can't do, but what you're looking for is quite basic and I'd imagine that it would work fine.
Once finished you can upload your video directly to a number of hosting sites including YouTube and
Vimeo. I mention Vimeo because they use HTML5 so anyone can watch their videos on the iPad or any other mobile device or computer.
Welcome again and enjoy!