How do I choose the correct model for a regression? So the central question of my project is to what extent does a country's level of export contibution towards GDP (i.e. exports as a % of total GDP) affect its GDP growth.

I'm comparing this hypothesis for two different countries, China and India.

I have annual time-series data for exports as a % of total GDP for both countries and their GDP growth for the last 30 years, but I have no idea how to choose a correct model to begin to anaylse it with.

I was thinking of pehaps using Autoregressive model one, any thoughts? If this is correct then I how would I begin to model it using my data?
Plot things. Do the raw data look like they have cycles? (I assume so, given that you are talking about economic data and want to use an autoregressive model.) Next, try to get the order of the autoregressive model by taking differences until the cycles disappear. This can also be tested formally using (a version of) the Durbin-Watson test. There will likely be further patterns. What do you see? Does the variability stay constant over time (likely when you have percentages) or is there a tendency for the variability to grow? What smooth (and simple) function follows the general distribution of the data? Fit it, assess the fit, repeat with different functions, until you have something reasonable.

Model selection is far more of an art than a science, and there often are several reasonable models that you can use.