I may be a bit overboard on the hardware and software targets. Taking a second and third look at your example video tells me that yes there is some animation s/w but the composite level does not appear to be as intense as I first thought. In any event you won't go wrong with the h/w I recommended but if you are on a budget you may be able to scale it back some. Certainly the basic system should be at least a i5 core 64 bit machine with at least 12 GB. Again, asking the folks that are actually going to edit your video should be the most important input on what s/w and h/w will work for them. I am assuming that you are going to have seasoned professional editors to do this work as the work you are targeting is not trivial nor is it something that you can learn fast.
The CERN video has more than one piece of software in it as there is a ton of animation, and a ton of compositing as well as multi synchronized track motion not to mention some very good motion graphic titles.
I would not start with buying software. Instead I would let the expert people you hire to choose the software they know and trust to get the job done.
Likely they will ask for one or more of the following and then some animation tools that will plug into these. You don't mention hardware but to render something like this CERN video you will need at least an Intel third generation i7 Core 64 bit CPU with a great GPU card that has 1 GB or more local memory and 16GB to 24 GB for system memory.
For Windows systems: Avid, Adobe Premier, Vegas Pro, and additionally Adobe After Effects no matter what editor you use.
For MAC systems: Final Cut Pro and Adobe After Effects.
Again, let your experts decide on the tools they need, don't hoist some one else's opinion on them.