There is basically no light kits used in that video.
He's sitting right in front of a window. Depending on time of day and/or curtain type used, you can get the best soft lighting by just opening your window curtains/blinds, and the camera is white balanced to the daylight at around 5600K-6500k. The camera used is a DSLR, lens used is probably a typical zoom kit lens included with the DSLR and shot at around 50mm as some have pointed out. The nasty yellow tint on his right face is a desk lamp right up on the wall behind him, hence the nasty blown out corner on the left screen. The camera is balanced at probably 5600K therefore making typical household lamps (balanced between 2900K-3200K) look extra fugly in yellow.
There you go, he's got no light kit and a DSLR + kit lens. If you're still interested in light kits there are options depending on who/where you ask, and prices can go around $3K-$4k for a professional kit offered by Kino Flo or Arri.
Also, most DSLRs have amazing sensors nowadays that you don't have to get F1.2 or 1.4 lenses, 2.8-4.0 will work just as well for what you're doing and save a ton of money. Since the sensitivity is great you're also saving money on requiring less light needed for a shoot. Hell, you can make a professional looking Video Blog for about $800.
I know most people will say Canon 5D Mark II/III, but it's like buying a Porsche to go to the 99c market for what you're doing...
Here you go:
Camera: Canon EOS T3i with kit lens = $650-$700 (probably have rebates too)
Light kit: Three of these
chinese made LED knock offs of the LightPanels brand @ $34 each X 3 = $102
You can skip the stands, they're light enough to clip or tape to something and they're LED so they don't produce noticeable heat. They output daylight balanced light (your mileage may vary with the color temp shifting over extended use in a year's time or so, but they are knock-offs and $34 after all), they also come with CTO filters so you can match the "ugly yellow" lights in your home if that's what you have. It won't look "ugly yellow" if you've balanced all your lights to as close of a temperature as possible with the camera.
So now you've got a cinema style camera with that shallow depth of field and a three point light kit with filters to match your surrounding as best as a $34 light can offer.
You may also want to skip any poor man's light kit that plug into the wall when doing video such as the compact flourescent lamp varieties. You'll experience nasty hums and various other frequencies in your audio recording. All DSLR on board audio is pathetic to begin with, don't add problems to the equation. And lastly, composition is key. Millions of dollars on lights and cameras won't do any good if your composition stinks.
