Change default Preview window size?
You might want to check out this question: What window management options exist for OS X?

My recommendation, if you want it to be fully automatic, is to use Slate.

Slate is no longer in active development, but it still works and is highly customizable. Put this code in a .slate.js file in your home directory:

var rightHalf = slate.operation("move", {
   "x" : "screenSizeX/2+screenOriginX",
   "y" : "screenOriginY",
   "width" : "screenSizeX/2",
   "height" : "screenSizeY"
});
slate.on("windowOpened", function(event, win) {
    if (win.app().name() === "Preview") {
        win.doOperation(rightHalf);
    }
});