Can I customize customer profiles?

I am building a eCommerce site for shirts and would like customers to be able to build a profile by answering specific questions (ex. favorite size, material, and colors). So after they build a profile and are logged in, only products fitting these exact preferences are displayed. For my profile, since I am short and thin, only small shirts that fit my size would be displayed.
Is there a plug in that does this? Or how do I go about this? Sorry if this is a basic question. This is my first wordpress site and I am learning as I go. Thank you for any help/guidance. I really appreciate it a lot.