Selecting a model type is based on the dependent (target) variable. The type of data that you are trying to model will determine which types of models you should be using. In my opinion there are five types of data. As a side note, there are many types of models however I will only cover a few popular model types.
1. Continuous Data
2. Categorical Data
3. Time-Series Data
4. Pooled & Panel Data
5. Curve & Surface Fitting Data
Each data type has a base model with a set of assumptions. If any of these assumptions are violated then a developer should move on to another model type to adjust for the violated assumption. A great example of this is for continuous data. The base model is OLS. One of the most common assumptions that are violated is the assumption of homoskedasticity of the error term. When this assumption is violated OLS is no longer BLUE (Best Linear Unbiased Estimator). There are a variety of solutions however WLS is a popular choice to correct for the heteroskeasticity in the errors.
In the video I cover a more thorough discussion of the five data types and models associated with them. Below is a list of a few popular models to go with each data type. Again, the data type and assumptions that are violated will all help to select the model type. There are cases where multiple types of models can be used and in these cases it is best to build two models and compare the results. One example of this is modeling PD (Probability of Default) in credit risk. The most popular method by far is Logit however there are a few papers that show examples where OLS outperforms Logit. There are a few issues with using OLS for PD such as the issues of OLS not being bounded by zero and one.
1. Continuous Data: OLS, WLS, FGLS, Polynomial Regression
2. Categorical Data: Logit, Probit, Tobit
3. Time-Series Data: ARIMA, GARCH, OLS, ECM, VECM
4. Pooled & Panel Data: First Difference, Fixed Effects, Random Effects, Mixed Effects
5. Curve & Surface Fitting Data: Splines, LOESS, Kernel Density
If you want some technical video on different types of models, check out Ben Lambert. He does a great job at teaching technical topics.