While the above listed primes are wonderful lenses, the reality of producing videos is that you aren't always going to be in a situation with an interview subject where you get to move the camera backward or forward to get the perfect framing. Or have the time to try different prime lenses until you find the focal length that best works out. Let's say you are doing one of your interviews in the subjects office and it doesn't have enough room to back up enough to frame the subject properly for the given environment. Yes, having a whole bag full of lenses would be really cool, but not really likely. This is where a zoom lens comes in.
I have done many of these types of interviews over the years. I do professional sound mixing for video productions and I can't tell you how many interviews like the one I stated above I have been a part of. And in every single case there was a zoom lens used. It's only been recently since the introduction of the Sony F3 that I have done an interview where the camera owner/op used a prime lens. And in that case he had three, a 35mm, a 50mm and an 85mm. Three great focal lengths for sure. But in that particular case we had to totally rearrange the room to fit the focal length picked. Luckily we had a lot of time to set our shot and do a ton of work. That meant moving a lot of furniture. Maybe you can do that in your situation, maybe you can't. Maybe you subject doesn't want you to tear apart their office just to do an interview.
When I have been a part of DSLR interview shoots the two most commonly used lenses were the Canon 24-70 f2.8L and the 70-200 f2.8L. With those two lenses on a 5D2, you'll have a huge focal range covered and they will allow you to do a lot of work, quickly while only carrying around two lenses as opposed to a whole suitcase full of expensive primes.
Yes, prime lenses give you some abilities that zooms just can't give you, but the converse is also true.
In the end, it's a balancing act, how much money do you have to get the biggest bang.
If I had to suggest only one lens, I'd say go with the 70-200 f2.8L. On a FF body that focal range will give you the ability to do a lot of different shots. But if you had the room in the budget for one more lens, then I'd say get a Canon 50mm f1.4 as well. It's speed can be a shot saver and it's a very nice and useful focal length.
But only you'll know the environments you'll be shooting your subjects in. Maybe the wider 24-70L and a 85mm prime would be a nice pair of lenses for you.