Unless you are going to use the shape animators there is no reason at all to change an imported Illustrator layer to a shape layer. None. In many cases changing to a shape layer is a distinct disadvantage. For example an Illustrator file filled with a gradient will loose that gradient. It would be helpful to know what tutorial you are watching. It would not be inaccurate or pessimistic to say that most of the ones that you find on YouTube teach poor and ineffective techniques. Some are just plain wrong.
If you click on the layer color in the timeline you can change the color of the outline of the shape path. If you don't want to see the layer handles then you can use the View menu to Hide Layer Controls (Ctrl/Cmnd + Shift + h) but this makes it difficult to figure out what you have selected. If you are working with masks and not shape layers you can choose Cycle Mask Colors in the preferences panel to make multiple masks on a layer easier to work with.
The most important thing to learn about working with After Effects is how to set up your project and your source files. I design more than 90% of my Illustrator for AE projects to that everything I want to animate is on a separate Illustrator layer and in it's default or final resting place on an illustrator artboard that is usually the same size as the comp I plan to work on. There are other things to consider when designing for video in Illustrator. For example you don't what to have a lot of single point strokes on your layers because they don't like to translate to clean lines when converted to pixels in video. You should have all small details snapped to the pixel grid in AI and for certain types of elements it is important to make sure that the size of the element is an even number pixels(points) high and wide so that these elements line up precisely with the pixel grid. There's a lot more to designing for video than just throwing a few things on the artboard and then trying to sort them out in AE.