I need help choosing the optimal fit for a dataset with $13$variables$.$Assignment says I can pick either a first$-$order linear regression or a polynomial regression, and I should use RMarkdown.

I know some functions of RMarkdown, like the ggplot and lm functions, but I don't know how to choose for multiple variables. There are so many different combinations of variables that are possible, and I have no idea which variables are best included and excluded and which variables could combine together like $($variablea$*$variableb$).$ How do I find the optimal combination?

So far the best adjusted R$^2$ score I've gotten is $0\mathrm{.}9202,$ but other classmates have done better. How can I improve my results?