With an extremely common name like Kalinowski, you're going to have a very difficult time unless you know exactly what you are searching for. You are not related to by far the majority of the many, many people who have that name. It's not a name that's associated a single family or a particular place. Also, unless your grandparents had extremely bizarre first names, there are likely to have the exact same name as dozens or hundreds of other people in their generation.
Really, unless you know the exact places where they originally came from, you have a very tough row to hoe. There are about 32,000 people with that name within the present-day borders of Poland, plus countless others in former Polish territories and abroad.
Don't waste your money on genealogical websites. They are exceeding unlikely to have any useful information that you would be able to find. Unless you have a specific place of origin, you may well have to be satisfied with the answer that they came "from some place in Poland". Most grandchildren of Polish emigrants are in the same position. Once the grandparents die and can no longer provide concrete information about themselves, the chain is cut and it is often impossible to do anything at all.
Also, beware of charlatans who promise that they can find information about your family, and there are a lot of them out there. A real genealogist would probably turn down your case as hopeless unless you provide them with a stack of documents to work with.