When do I choose what regression? Do I just choose which has the better determination coefficient R2 when I'm fitting them over each other?

Let's say I have 10 test series with about 6 datapoints each. To get those datapoints an equation using a specific variable must be solved. This variable is different in each test series and differs. When trying to gauge and choose a regression for each one of these test series how do I see when the regression model I am using starts to change? Maybe the first few adhere to the linear model, but they start going towards logarithmic or polynomial model.