How to determine which features matter the most? I have a large dataset that consists of search results of loans. Someone would input their details like income etc and the results would include a bunch of loans from different companies and different loan types (so there can be more than 1 loan per company).
The dataset consists of every unique search and all the corresponding results. I also have a column that shows which loan has been selected at the end by the user per each search.
I am looking to find out which features of the loan were most important to users, i.e. try to predict what loan the user will select depending on his/her inputs.
What ML model could I use for this? I am unsure how to approach the problem.
One common approach is to use Principal Component Analysis (PCA) and drop the directions with less variance. See here for instance:
Using principal component analysis (PCA) for feature selection

The latest version of sklearn allows to estimate the feature importance for any estimator using the so-called permutation importance:
Permutation feature importance
Random forest in sklearn also have other methods implemented to estimate the feature relevance:
Feature importances with a forest of trees