Suggestions for binary classification algorithm
I would say support vector machine, support vector classifier. This will allow you to have as many predictors as you want. Also, you can improve your accuracy by tuning your model parameters. 

Here is another nice link for support vector classification

Since you did not mention any language, I would use python as there are so much online support and you resources available online. 

I would also check xgboost classifier. 

Let us know how did it go.