The command mode is not useful to complete environments. You always have to type some letters of \begin, and invoking the completion mode will result in a huge list of environments tags. On the other hand, environments are so often used that Kile offers a special mode to complete environments. Forget the opening tag and write, for example, eq.

When you call the completion mode with Edit->Complete->Environment or keyboard shortcut Alt-Space, the opening tag is automatically added and you will see \begin{eq}. After this change, the completion list is much less cluttered.

Completing a LaTeX Command

Now select an environment, and you will see that it is also automatically closed. Even more, if Kile recognizes it as a list environment, it will also insert a first \item tag.

Completing a LaTeX Command

Go to Settings->Configure Kile...->Kile+Complete to configure one or more of these lists. This mode uses the same word lists as the completion mode for TEX and LATEX commands.