How can I describe in a single word or two words a person who is sensitive in cost-effective stuff or products? Or persons who care the most for cost-effective stuff?
You can describe such a person as being economical:
1 : marked by careful, efficient, and prudent use of resources : thrifty
// an economical shopper
'resources' here includes money which is available to spend.
I would say bean counter.
From Urban Dictionary:
Beans are a cheap commodity, so to count them is a rather silly thing to do. A "bean counter" is one who nitpicks over small things in order to save costs. It is a derogatory term for accountants, bankers, and anyone who holds a financial interest in an endeavor.