a supermarket as good as you can find anywhere else in europe and america , called Prostor where you can buy anything you may think of in just one shop. There is two main public markets , one for food recently refurbished to ver good standards and the other is for clothes and all short of household items. Beware that imported items are as expensive, if not more than in the UK and in particular whisky and champagne can reach astronomical prices but if you stick with Vodka(much better than over here , particularly Nemirof and Olimp) beer and local champagne you will not be dissapointed.
Also beware before travelling to Kremenchuk that you are going to an industrial city ,the town centre is very beautiful and full of options but the outskirts are full of factories as you are not in Crimea. I certainly have travelled a lot over there and do not believe at all that it is a dirty city and people are welcoming (if you behave with respect to them because it is their town where you are visiting) , certainly I do not have nothing negative to say about ukrainians in general and Kremenchuk in particular.I marry my wife over there and we like to get back as much as we can ,and we enjoy visiting there every time. If you need any specific information, feel free to ask and we will like to help if we can