First touch would be helpful to see how customers first got introduced to your brand. Participation allocation would help you see the in-between marketing activities, and it would also help you see what pages they saw before making a purchase. You could look at how many visits users have before making their first purchase, and how many visits they do between purchases.
Site (internal) search data could help you find what users are looking for, and what might be hard for them to find.
If you have recommender or comparison tools you could see if users who use those tools are more likely to purchase.
