Most programs should remember window size from loading to loading. E.G., when you close iTunes or Firefox or Safari, the next time you open it, it should be in the same size and location.
OTOH, in general, most Mac apps don't believe in full screen, for a wide variety of reasons that have been beaten to death on this forum over the years. The green ball in the upper left tells a program to toggle between its current size and the size it considers optimal -- this varies from app to app. Some choose to become as big as possible, other toggle to a minimal mode (e.g. iTunes), and others adjust to fit content (e.g. I think most of the browsers adjust to fit the width of the page and the height of the screen).
Give it a try for a while and see how you get used to it. I honestly don't miss full screen much when I'm using OS X.
Now there might be a few apps that don't remember the size and location you specified -- if that's the case, you should complain to their developers to fix it. If all of your apps are doing this, there might be something wrong with your user account....