You can see what SMS and MMS backup applications are available in the Play Store that do what you are looking for. Another option to check is if you can use Cloud Print to send the message conversation to your printer.
If you just need the pictures, save the images to the phone's Download folder. Then connect the phone to the computer using a USB cable and drag and drop the pictures from the phone to the computer.
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.