I am an Adsense publisher since 2009. As all publishers around the globe, I have listen and read many Adsense optimization tips (I understand that G Adsense hopes to help us maximize revenues as it maximize there's as well). So we've tried, tested and monitored the results of these recommendations. And guess what? I am still not sure that the results translated in an increase in revenue. It is fluctuating and confusing. Must ad that a serious factor to take in consideration is the user experience, which include - time on site, BR and page/visit.
So far - TYPES: Types that I have tested so far are: large and medium rectangles, wide skyscraper and big leaderboard. Link units and search form are site specifics - depends on layout and design.
Best performers: Publishers always check ad revenues to learn now much each of Adsense Ad Units is earning. Generally, the first Ad Unit, above the fold, often gets the highest pay, while the second is much lower and the third is much much lower.
HOW MANY ALLOWED: It is allowed to have 3 AdSense Units Per Page. In certain cases, you may get an approval to put even 4 as long as single one is above the fold and the page is long enough.
Amount of ads: This is the actual question here. It varies. I have never came to a conclusion about the amount of ads to put per page.