Optical stabilization (OS) in a lens uses motors to shift the position of one of the inner elements, in response to signals from accelerometers (the same as the sensors in your cellphone that know which way to rotate the screen) and tries to keep the image projected onto the sensor as still as possible, even if the camera itself is wobbling about a bit - such as when you're hand-holding it. It's designed for still photography
at slow shutter speeds. In video work it creates a whole other set of problems, as you will have two possible scenarios:
- The camera is on a tripod - OS must be turned off or it will tend to start adding motion where there isn't any.
- You're shooting handheld or on a stabilizer rig, and you will pan the camera. Now the OS has a problem because it will start off trying to keep the image still, but will rapidly hit the limits of adjustment and suddenly snap back into the center. Instead of a natural 'handheld' feel to the shot, it will be still...still.. still.. BOINGGGGG.... still... still.... and it looks terrible.
A lot of good advice already about lens choices, but so far nobody's actually asked what you will be shooting, and how. A fast EF-S 50mm (or full-frame EF 35mm on your crop body) will give a field of view roughly the same as your eyeball, so for example you can shoot a full-length scene from about 20 feet away. If you're capturing wide landscapes, home interiors, or working in small venues (e.g. filming a local band in a bar) then it's much too narrow a field of view, and you'd be looking at something around 16mm to 20mm. As a general-purpose lens on my crop bodies I use a Sigma 17-50 2.8 DC (outside of your budget but worth scouting for a second-hand one). It has OS for stills and a constant aperture. Some people get addicted to vintage glass (I have a growing collection, on a 5dIII an old Pentax 50/1.4 is hard to beat) but I wouldn't suggest it for a newcomer as there's a lot of dud glass on the used market, you really need to know how to service them yourself to get rid of the dust and fungus.
Bear in mind as well that normal Canon 'stills' lenses never
have a mechanical aperture ring, so you must always change it using the command dial on the body. That's necessary for shooting in Tv or P mode, a little fiddly for video but not terribly so. Dedicated video lenses, on the other hand, only
have a mechanical aperture - you cannot set it from the body, so you can only shoot in Av or M. Most also have a 'declicked' aperture ring that allows you to choose any position, not just the numbered f-stops. That's useful for video as people like varying the aperture as they shoot to adapt for lighting changes, but it's assumed you would be fitting a set of rails and a follow-focus system to keep it under control. It's possible
to shoot stills with a video lens but it's a hassle.
The T3i/600D has a very important feature for video which can drastically affect lens choice. Normal video will have a lot of moire and aliasing (jaggy lines and color patterns on diagonals and finely-textured objects); that's just the price you pay for shooting video on a Canon DSLR - but the T3i can switch to 3x 'crop video' mode - it zooms in by 3x but the moire goes away completely
. This gives a huge improvement in quality and still shoots in full-HD, but the extremely narrow field of view means you have to work with an ultra-wide-angle lens so the cropped region from the center isn't just showing someone's left nostril. If you install Magic Lantern to shoot raw video on the T3i (not in HD but decent enough) that will also crop the sensor. All this means with video it's easier to start with an ultra-wide and make it into a longer lens "electronically", than fit a standard 50 prime and have to stand half a block away.
My best suggestion - if you're not sure which lenses will suit you best, don't buy anything
one for a weekend or borrow one from a friend, see how it feels, try something else next time. If (with respect) you don't have any friends with a shelf groaning with L glass, check out things like photowalks where you can spend an afternoon with a bunch of like-minded people and their backpacks