Should I scale my features?
It is not necessary to scale your numerical values when using linear regression. However, people still do it since it can speed up training if the algorithm uses gradient descent and it might make your coefficient and intercept terms more interpretable.

You can read more about it here: https://stats.stackexchange.com/questions/185624/feature-scaling-normalization-in-multiple-regression-analysis-with-normal-equa

On another note, there are a lot of binary classifiers that will give you a probability instead of a binary output. For instance, in sklearn many binary classifiers have a predict_proba method that does just this. I can recommend random forest.