Single word for shopping after comparing price and features across multiple shops and product types

The standard phrase is...

shop around - to compare the price and quality of the same or a similar object in different shops before you decide which one to buy.

This chart shows how the expression has become increasingly common over the past century, and here are thousands of written instances of [you] should shop around (standard consumer advice).

In the US, the term comparison shopping is fairly standard, as reflected in this article about comparison shopping websites.

There's informed purchases and bargain hunting. Making the shopper an informed buyer or a bargain hunter, respectively.

"Due diligence" is a phrase that captures most of what you are looking for. This phrase doesn't apply directly to shopping, but it represents the work that is done before making a final decision.