First I suggest that you go to www.dofmaster.com/dofjs.html
and plugging in your numbers.
Shooting wide- like at 18mm- is going to result in a not so narrow DOF as compared to shooting long. Aperture has some to do with it- but NOT so much as most believe. You get better effect using longer lenses than you do short- and the aperture comes in a distant second. This is why it's harder to maintain focus at longer focal lengths in the first place- shooting wider gives you more DOF - easier to stay in focus.
So, the answer to your question is to get a longer lens over shorter- real wide is self defeating.
DOF with video on a DSLR works like DOF with photos on a DSLR- because we are using the same sensor.
Personally, if you are looking at video- you should be looking at the t4i with the 18-135 STM lens. The 18-135 STM lens is quiet- but I would suggest working it at the longer end.
Using the kit lens @ 18mm and f/3.5- at 10 feet- your DOF is about 21 feet. Wide is not a good solution for thinner DOF.
If you take 50mm at 1.8- @ 10 feet - your dof is 0.81ft. Using a f/2.8 zoom- 1.29 feet. @ f/5.6- 2.62 feet.
Using a longer lens - like a 85mm- at even a slightly longer distance- say 15 feet- gives you 0.63 feet @ f/1.8, 1 foot @ f/2.8 ( zoom ), 2.01 feet @ f5.6 ( kit lens) .
At the long end of the 18-135 kit lens- @ f/5.6 @ 15 feet- your dof is 0.79 feet.. Even at 25 feet- dof is still only 2.21 feet.
End result- more focal length is more important overall - IMO....
Just like photography, you need to consider your distance from the camera to the subject and from your subject to the background. In the end, a fast zoom is still better than the kit lens- but a zoom is still more versatile when it comes to framing and composition. Personally, I'd buy a kit lens - with longer focal lengths and consider fast primes only as a tertiary option- unless you are shooting primarily at one distance where the framing never changes. Upgrading the kit lens is like a double edge sword.. Faster lenses- more limited range & limited composition possibilities. For example, with what you want- limited DOF, I would not suggest going to a 17-55 f/2.8 for video- as you would probably be better off with a 24-70 f/2.8 instead- because longer focal lengths will help you accomplish the desired effects more easily.
If you decide to go with a prime- the older primes that are manual only- tend to have longer throws (more turn on the focus ring ) - making it easier to achieve critical focus.
Edit: after some additional thought- ideally- I'd get a 18-135 - mainly for the wide end ( where it does not matter ) and for the longer end, and maybe two primes- a 50mm and a 85mm. If the primes work for a shot- then use the longest one that works for the shot- otherwise your zoom would catch the extremes.
EOS 5D III, EOS 7D,EOS Rebel T4i, Canon 70-200 f/2.8 IS II, Canon 24-105L, Canon 18-135 IS STM, 1.4x TC III, 2.0x TC III, Σ 50mm f/1.4, Σ 17-50 OS, Σ 70-200 OS, Σ 50-500 OS, Σ 1.4x TC, Σ 2.0x TC, 580EXII(3), Canon SX-40, Canon S100
Fond memories: Rebel T1i, Canon 18-55 IS, Canon 55-250 IS, 18-135 IS (Given to a good home)...