Choosing best methods for estimating the unknown parameters in a linear regression model
After the Data Munging, this is the most difficult task on a prediction model. However, in order to answer it, we need more details. What do you mean by the "best model"? Do you want accuracy and long training time? Do you need something really fast with lower accuracy? Something between the two of them? What are your features? Have you just taken them or have you created new features from them?

In any case, I suggest that you should spend some time and read this perfect tutorial from Microsoft about Machine Learning. A part of the tutorial to understand what I mean:

Regression


Ordinal regression: Data in rank ordered categories
Poisson regression: Predicting event counts
Fast forest quantile regression: Predict a distribution
Linear regression: Fast training, linear model
Bayesian linear regression: Linear model, small data sets
Neural Network regression: Accuracy, long training time
Decision forest regression: Accuracy, fast training
Boosted decision tree regression: Accuracy, fast training


When I have a similar question and I don't know which one to choose, I usually end up to 3-4 different algorithms based on the cheat sheet of Microsoft or the one from the scikit-learn, try them all and choose one or two of them with the best results.