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Contacts: Are all of your contacts associated with your Google account, or the local Phone account? If they're associated with Google, then they're in your Google Contacts in the cloud, and will automatically sync to your new phone once you've logged in with your Google account. This is very easy, and one of the reasons I always recommend using Google Contacts. If they're saved to the local Phone account, you'll need to open the Contacts app on the S2, tap Menu, and look for the Export function. Export the contacts into a .vcf file, then copy that file from the phone to you computer (via USB). Go to your Google Contacts on the web, then import the .vcf file. Once the contacts are in Google Contacts, they will sync with the new phone.
Videos/Photos: Connect your S2 to your computer via USB, and use Windows Explorer to drag and drop these files to the computer hard drive. If they were all taken by the Camera app, they should be in the /DCIM/Camera directory on the phone. Then connect the S6 to the computer via USB, and copy the files from the hard drive to the phone. You should be regularly backing up your photos and videos anyway, if they're important to you.
Apps: Any app you've installed or purchased from Google Play Store or Amazon Appstore can be installed again on the new phone, as long as you're using the same account. The app data might not be available, though, if the app doesn't save your data to its own server in the cloud. In that case, you could try using
Helium to backup your app data, then restore it to the new phone. Be aware that some apps on your S2 might be outdated or no longer available, which means you may not be able to install them on the new phone.