You should wait until the paper is completely dry before removing it from the block. Most manufacturers leave a few centimetres unglued for this purpose. Good watercolour paper has a neutral pH or is acid-free. Acid is commonly used to manufacture paper and it is this acid that turns ordinary paper yellow with time. In the past, paintings on paper were notoriously fragile, but modern paper-making technology has solved that problem.
Paper is available in different surfaces.
I use mainly a rough surface. I find it takes the paint well and is suitable for a loose approach. Smooth paper usually allows for more details. If you're into detail, try the smooth paper first. As with most art materials, paper's quality depends upon its price.