For landscape photography, would suggest that u get yourself a tripod too.
Anyway, like what others had said, for outdoor photography when there are abundance of light (natural or otherwise), F4 will be enough. However if you are shooting indoors that lighting are not that abundance or when needing to shoot in low light condition, then f2.8.
Actually whether or not IS is required is up to you and your shooting techniques. I personally find that I can go without IS for as long as my shutter speed was not below 1/20 at 200mm range.
On a personal note, if I can choose again (I got the f4 version), I would definitely go for the 70-200mm f2.8L non IS and add a monopod if necessary.
That should be fine. I really regret not getting the f2.8, because at that time I was thinking that IS is so so so important. But later on, I find that I can actually handle without IS. And if the lighting are too dim and my shutter speed was too slow, even with the IS, it would not do much help.
In my case, I would rather have my monopod, it is more flexible and quicker to setup than my tripod. I only use my tripod when I am taking very long exposure, all the other can be accomplish with my monopod.
I think it's better to handle one such lens before concluding that u do not need IS. 1.4kg is not something easy to handle while focusing and framing. And not to forget how long you are using it in one shooting session. It can be very hard to have steady hands after holding it ard for hours...