If Google Play Store is not installed, then the device is likely not certified to use it, and there will likely be problems with compatibility. But you can try downloading the apk file for the latest version by searching Google for "Google Play Store apk." Then tap that downloaded file to install. You have to make sure you have "Unknown Sources" checked on in the Settings>Security menu.
If Google Play Store doesn't work, then I would stick with Amazon Appstore. Using your phone's browser, go to amazon.com/amazonappstoreapp, and follow the directions there