Creating a Feature to determine popularity
You need to put your shoes into business people and communicate with people from that department on regular basis, trying to understand what the business's needs are. In e-commerce your second metric is Conversion Rate and is defined as:

CR = Orders/Views*


Please note there that there are two variations of Views. One that comes from Product List Page (aka PLP) that is mostly know as Impression, or the one comes from Product Detail Page(aka PDP) is where the user actually lands on the product detail page. The latter is more common in the CR calculation.

Your first one i.e. the popularity, that somehow I liked, can be used. Only be careful that it is going to be affected by number of items available in that category. 

In general, I find it useful to think about edge cases when coming up with new measures and to see whether the resultant is desirable. What do I mean by edge cases, let's take your popularity score, by your definition, for example. Imagine the following two scenarios:


popularity item 1 = 1/2 (very limited items in this category where item 1 is)
popularity item 2 = 1000/2000 (large number of items in this category where item 2 is)


What you see here looks quite normal by the original definition from mathematics perspective. However, what it means from recommendation/business perspective that you have similar scores from two items from two different categories. Here the business may jump in and say looks we have a lot of more assortments in the category where item 2 is and often items in this category are in the warehouse or have faster delivery etc. etc., then we prefer our products from there to be recommended first. This is the point you realize that while results seem reasonable, at least according to the popularity definition, falls short on certain aspects. 

Other ideas: I noticed you are leaning towards using multiple scores. That is a great idea. Having multiple factors may catches these corners and address multiple business needs at the same time. Like having both CR and popularity. Or may think of each item's profit contribution to the business and take that into consideration. Imagine you have a score in place that gives equal chances of recommending an iPhone or Wireless Mouse, however iPhone contribute way more to the business (it is more profitable), then you may want to push for that factor too. You may also like to look at Impression I mentioned if it is available from your tracking. Item's rating, delivery, Add_To_Cart, Wish_List, or Time_Spent_on_Item are other things to think about. Check this post to get some other ideas how things are roughly done in Amazon. Hope these help.