Update (2016-04-20)
The add-on LaTeXify now adds two commands "TeXify2PDF" (which runs BibTeX and TeXify+dvips+ps2pdf with LaTeX engine) and "LaTeXify2PDF" (which runs Biber and TeXify+dvips+ps2pdf with LaTeX engine) to accomplish your needs.
Original answer
Follow these steps to have a menu entry, a keyboard shortcut and a toolbar button for an accessory that runs LaTeX -> dvips -> ps2pdf in WinEdt 8.
Show the "Options Interface" (Options -> Options Interface)

Double-click the "Main Menu" item (MainMenu.ini gets opened)
Just before the line
ITEM="Compile"
add the following lines
ITEM="dvi2ps2pdf"
CAPTION="dvi2ps2pdf"
IMAGE="TeXIconRed"
SAVE_INPUT=1
MACRO=`Assign("Old-PDFTeXify-Method","%$('PDFTeXify-Method');");`+
`Assign("PDFTeXify-Method","2");`+
`Exe('%b\Exec\TeX\PDFTeXify.edt');`+
`Assign("PDFTeXify-Method","%$('Old-PDFTeXify-Method');");`+
`Release("Old-PDFTeXify-Method");`
SHORTCUT="24665::Shift+Ctrl+Y"
REQ_FILTER=:"%!M=TeX"|"%!M=TeX:STY"|"%!M=TeX:AUX"
ITEM="-"
Press Shift+Ctrl+F9
Now (in the "Options Interface") double-click the "Toolbar" item (Toolbar.ini gets opened)
Just before the line
MENU="ConTeXt"
add the following lines
MENU="dvi2ps2pdf"
MENU="-"
Press Shift+Ctrl+F9
Now you have a toolbar button in the drop-down button containing all the compilers

a menu item in the "TeX" menu

and a shortcut (Shift+Ctrl+Y) to run LaTeX -> dvips -> ps2pdf automatically.