Filmed the grandkid with both the EF-M 22 and EF-M 18-55 in the last year. The 18-55 with IS wins hands down when going handheld for movies. I'd only shoot the 22 with a fluid head on my tripod - my wife get nauseus easily. I do have a fluid head for my FF rig but that defeats the purpose of using the M for me.
Did some quick experiments in my office panning the walls and moving from near to far objects and back with a few lenses. Nothing definitive, just a quick look to see how they did through the viewfinder.
The EF-M 18-55 was the best. The IS on the EF-M 11-22 and EF-M 55-200 smoothed the motion. AF on the 11-22 was quick and accurate, but seems to hunt more on the 55-200 as you might expect. The AF on the 22 was good, but the motion was a bit jerky with no IS.
I also have an old FD 35-105 converted to EF mount. It works well if you can handle manual focus since it has 180 degree throw. At 35mm and f/3.5 it has lots of DOF so pre-focus is possible. No IS so a tripod would be good. My quick test was ok at 35, pretty jumpy at 105. This is probably representative of any old MF lens mounted with an adapter since they don't have IS.
Did a similar test with my EF 24-105L which I have used on my 6D. Autofocus is pretty jumpy and noisy - the internal mic picks it up in my past experience so I use an external mic. However, the IS makes all the difference, smooth movement, no jerkiness so I just turned off the AF and manual focused in these tests. It doesn't have quite the focus throw of the FD lens so it might be harder to nail focus. The new 24-105 IS STM would be something to consider for video.
Also tried the EF 40. Autofocus was a bit quieter and smoother than the 24-105, but it seemed to hunt more in my simple test panning around the room and was a bit jumpy to watch. The lack of IS might also affect AF. I also tried my EF 35L and found it did better than the 40. AF noise was low and it didn't seem to hunt near as much. Seemed less jumpy, but that may be inertia from the extra mass ;-).
The EF 17-40L with no IS was ok at 17, but lots of hunting at 40. I wouldn't use it for video on my FF either. I may someday consider the new wide angle zooms like the 16-35 f/4L IS if I do more FF video, but the M seems to be my primary video camera for now.
So I'd suggest a lens with IS if you plan to handhold at all. If you want to use autofocus then I'd stick with EF-M or EF STM lenses for the silence, even with an external mic. The EF-M 18-55 sure seems like the best bet in your price range at this time. The other option would be an adapter with a good manual focus lens to get some experience with manual focus and no IS on a tripod.