For starting out in DSLR video, the 70D is supposed to be the best bet for crop sensor cameras. It is more expensive than the 60D or the Rebel series but it has a much different kind of autofocus system that is optimized for autofocus while shooting video. All are good cameras but this is a major benefit. The 60D is at a low point in its price cycle. The Rebel series are generally replaced every year, although the t3i is a freak that continues to hang on. Some people will tell you that you have to buy a full-frame camera, but this is a significant investment and not necessary right away.
For lenses, consider those with "STM" in the name. The STM motor is supposed to be quieter and smoother focusing during video. That would mean choosing the 40mm f/2.8 STM over the older and noisier 50mm f/1.8. The "nifty fifty" does allow more light in, but keeping focus on a living subject at an aperture wider than f/2.8 is quite difficult. There are a number of STM lenses now, an 18-55, a 55-250, and an 18-135. These are all supposedly improvements over the prior non-STM versions. All of these except the 40 feature image stabilization.
There are also new prime lenses that feature image-stabilization but not STM, the 24mm, 28mm, and 35mm IS. They use a different kind of motor that is similarly quiet and smooth focusing. Optically, they are reported to be very good lenses for their cost.
If you are used to the zoom and autofocus of your camcorder, you may wish to get started with an 18-55 or 18-135 STM kit lens and see what focal lengths you prefer to use when shooting before you purchase a prime lens.
Some folks will tell you to buy new or vintage manual focus lenses so that you can manually control aperture and focus. Although there is a benefit to that, you may not be ready for that level of commitment. If you are doing run-and-gun documentary style video, autofocus can be a help. If you are doing art videos or controlled narrative shooting, manual focus may be possible.
EDIT: If I were getting started, I would choose the 70D, the 18-135 IS STM, and the 40mm, and use those before I made my decision on investing more money into prime lenses.