1. Select mode to select vertices/edges/polygons
2. Activate tool by hotkey, menu item or toolbar button
3. Manipulator shows with visual aid. For grab/rotate/scale, visual aid can be X/Y/Z. For extrude, visual aid can be Z.
4. Move mouse cursor to a convenient place and press a second hotkey to enter modal mode.

The point of the manipulator is to avoid having to use a hotkey, and to give beginners an easy way to get used to the interface. Making it show up when you press one of the transform keys, kind of (imo) get's rid of the purpose of having them there.

As a beginner user, I like LMB select. But RMB select has one clear advantage over LMB select that I simply cannot ignore: be able to select vertices/edges/polygons even if the transform manipulator is on the way. In a ideal world, I have both the LMB select AND be able to select object/components without worry about transform manipulator. Here is my proposal on how to achieve it: