which classification model allows user to choose importance of data inputs?
The answer is that  you don't need to . Say you decide to go with some classification model, for instance a simple decision tree, the model in question will implicitly learn which are the importances (or weights) of the features of your training data, and will use these features as main nodes of the tree.

To better understand this idea, lets take as an example the ID3 algorithm, which is one of the several existing algorithms to generate decision trees from a dataset. This algorithm will build a tree by iteratively setting as decision nodes those features that maximise the information gain at each step, or in other words, those that are the best predictors.

So it will implicitly be giving more importance to the attributes that are better predictors, hence there is no need to assign weights to the features of the dataset.

So my suggestion is that you try using some classifier from scikit-learn such as RandomForestClassifier for instance.