Welcome to Android Central! The easiest way to transfer your photos is to upload them to your Google Photos in the cloud, so that they can be accessed from any device that you're logged into: https://support.google.com/photos/answer/6193313?co=GENIE.Platform=Android&hl=en. If you don't want to use a cloud solution, then connect the old phone to your computer via USB and transfer the photo files using Windows Explorer to the computer's hard drive. Then connect the new phone and copy those files over.
SMS is harder. Your best bet is to use an app like SMS Backup & Restore on the old phone, then restore them to the new phone.