Which machine learning technique for product ranking/scoring
So I am assuming you just want to be pushed in the right direction. There are 2 different ways you can go about this.

Netflix up until very recently did all its recommendations using classical algorithms and setups, see paper on their architecture. 

For this type of light recommendation problem I would recommend using something from PredictionIO. It is very versatile and can be used to classify using a variety of inputs. It's also not very hard to learn. 

You can also solve this problem using neural nets, it can be viewed as a recommendation by classification. Deep learning is all the jazz now and you can utilize these breakthroughs in the recommender space.

Youtube is the big one when it comes to deep neural nets applied to recommendations, see this paper.

They split their system into 2 separate neural net models. One for candidate generation, and then another for producing the actual recommendations. 

Spotify also did some awesome stuff applying Convolutional Neural Nets to the actual audio streams with some equally interesting results: 
http://benanne.github.io/2014/08/05/spotify-cnns.html

As far as implementing something like that goes I would look for examples and build in python using either tensorflow or theano and keras. It wouldn't have to be too 'deep'. 

Hope that helped!