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There is an old rule from the film days, that the minimum hand held shutter speed should be 1/focal length. For 200mm, no lower than 1/200 second.
I print very large and am a fanatic about image sharpness. I try to never let shutter speed be lower than 4 times focal length. If I'm using a lens such as 70-200 f4L IS, which as rated as 4 stop IS, rather than use as low as 1/12 second (4 stops), I try to keep it at 1/50 or higher (two stops).
For years, I owned a 200 f2.8L, and fought with myself about trading it in for the 70-200 f4L IS. I loved the f2.8 aperture but wanted IS. I don't shoot night sports, where f2.8 is better, and IS won't help subject motion.
I bought the 70-200 f4L IS, and tested both on a solid tripod in full bright sunlight. They were about equal in sharpness. Then I shot the 200 f2.8L handheld at 1/800 second side by side with the 70-200 f4L IS at 1/200 second. The zoom was clearly sharper at extreme high enlargement (50% pixels). I also consider myself no better or worse than other photographers about hand held steadiness.
I now have a 500 f4L IS, 300 f4L IS, 70-200 f4L IS, 100f2.8L IS macro, and have been watching 35mm f2L IS, 28mm f2.8L IS, and 24mm f4L IS.
My suggestion is do what ever it takes to afford the 70-200 f4L IS. The IS is worth every penny of its cost in image quality.
PS I shot the Taj Mahal in 1978 using a 2 1/4" by 3 1/4" medium format camera, 150mm lens, tripod mounted (tripods were allowed back then).
I reshot the same frontal view Taj Mahal in 2007, using a Canon 5D, and Canon 50mm f1.4. I shot it hand held, at 1/3200 sec. The later digital picture was MUCH sharper. There simply was no comparison!