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As for crop factor, using an EF-S lens on a crop body such as your Rebel, there is no crop occurring. The lens is designed for crop bodies, so you get the full angle of view produced by the 18-135.
Ummm, no. It is true that the EF-S lens is designed to be used with crop bodies such as the Rebel, but its angle of views at 18-135 are still the same as an EF lens with the same 18-135 focal length. And the focal lengths are always compared to the 35mm equivalent, so the 18-135mm on a Rebel, will show the same angle of view as 28.8mm-216mm (18-135 times crop factor of 1.6) would show on a full frame, 35mm equivalent.
to the OP: what a good walk-around lens is for you really depends on what you tend to shoot AND how you usually view the results. If you're into nature shooting, that's usually in the medium to upper telephoto range (135-300mm). If you're into landscape, that tends to be closer to the wider angle side (12-24mm). If you're into people shots, then that's closer to 50-135mm. If you're into interior shots or nightlife, then a lens with a large maximum aperture (f/1.4-1.8) is probably what you should be looking for. And as mentioned earlier, the wider the range of the zoom, the less is the image quality. However, image quality is relative. If you're not going to be printing larger than 5x6, or showing larger than (say) 1200 x 800, then the resolution you will be getting with higher-quality lenses will be wasted. If you tend to crop your photos to extract the "best" framing, then you do care about resolution.
In my case, I have a Rebel T1i, and started with a kit lens. Relatively quickly, I upgraded several times, and ended up with a 24-105mm L-series lens. For MY purposes, it was the best compromise of image quality, weight, range and price. And yes, there are always compromises. You just have to decide what is important for you.