In WinEdt, the command 'PDFTeXify' is some sort of 'Quick Build' command (also exists 'TeXify' for the DVI cycle).
pdflatex and compile bibliographies, indexes and glossaries automatically to get a fully compiled document, that is something similar to:
pdfLaTeX + BibTeX + MakeIndex + MakeGlossaries + pdfLaTeX + View PDF
To customize it, you have to open the 'Execution Modes' interface ('Options' menu) and go the the 'TeX Options' page.
To obtain the equivalent of
LaTeX + dvips + ps2pdf + View PDF
you just have to check 'dvi -> ps -> pdf' in 'PDFTeXify Method'. Note that bibliographies, indexes and glossaries get compiled (when needed) even if you opt for this choice.
You can press the 'Help' button in that dialog to know more about the available choices.
For example, choosing 'Default' in 'PDFTeXify Method' and 'xelatex.exe' in 'Default PDFTeXify Engine' you get something like
XeLaTeX + BibTeX + MakeIndex + MakeGlossaries + XeLaTeX + View PDF
If you want to further customize the execution of the various accessories (e.g. change
biber) you have to go to the page 'Console Application'
I suggest you to press the 'Help' button here to know how to set the lots of choices you have.
If you want to add capabilities of compiling nomenclatures or inline Asymptote graphics to the 'PDFTeXify' command, have a look at these add-ons: Nomenclature and Asymptote.
Moreover, you can try the add-on LaTeXify which adds lots of buttons for this type of automated compilation.
At last, but not least, the add-on arara lets you launch the famous tool
arara from within WinEdt, if you would like to opt for this (which is probably the best tool for dealing with such automated compilations nowadays!!!).