>Should I install the Miktex first?
Yes. But you can also install it after WinEdt; WinEdt will then detect
that MiKTeX has been added to your system.
>So WinEdt is not an independent software
That's right, WinEdt is not an independent software working alone.
After installing MiKTeX, you might want to start up WinEdt, click on
"Document", then "Current Work (samples)", then "LaTeX demo". This will
bring up a sample file which you can send to MiKTeX to process by just
clicking on WinEdt's "LaTeX" button.