Welcome to Android Central! If you installed your apps from Google Play Store or Amazon Appstore, you'll be able to reinstall them on the new device, as long as you're logged into the same account. Game progress doesn't always carry over, though. For those games that save your progress to their own server, or to your Facebook or Google+ account (as long as you log in with those accounts), it's easy. But for games that save progress locally, it's harder. Sometimes, you can locate the saved game files by using a file manager app and looking through the various app directories. You can also use an app like
Helium to back up associated app data to your computer.