Hi Porky
If you are going to be there on a middle-long term basis , I believe that the option of a hotel is going to be expensive to you. At the town centre, there are three main hotels, one is called the Kremin which I shall not recomend anyone.... then a budget option very close to the train station called Dniprosky Zory and a top endo hotel which I never tried because was very expensive for me called Ontario.
Please beware that the Ukraine is not an english speaking country , though there are some people that speak english people over there do comunicate mainly in russian and ukarinian which is very useful for everyday life over there. If you are not familiar with the language , you shall seek help at least to set things up to your taste or othewise you will be dissapointed.
About going out, the town centre is full of options and there are places like the Liverpool , Chinese restaurant Pekin and others that have a menu in english. Others like Eden, Pelikan , Ukraina do not have it but they are as good as the others if not better and you will be quite pleased if you go with a local.
Shopping in kremenchuk has also plenty of choice , as previous people have informed you there is a market for food and other for clothes and household items. There is at Maladiosny (outside of the town centre)