The lessons of US involvement in the Philippines are very complex.
In a way, our involvement tells us that we should not try to conquer countries that want to be independent. We had to fight a relatively long and bloody war to subdue the Filipinos. However, we did win this war, which implies that it is possible to win such wars.
Our occupation of the Philippines taught us different lessons. It taught us that we could have a relatively good relationship with a country that we were colonizing. There were essentially no uprisings against the US once the initial war was over. This may be in part because we gave the Filipinos more autonomy than they had ever had before and because we promised them eventual independence.
However, these lessons did not seem to translate well to other conflicts. We were not able, for example, to replicate our success in the Philippines half a century later as we got involved in Vietnam.