Buy your own portable hard drive as if you ONLY have them on your laptop and that is lost or stolen or crashes you have lost everything.
Buy a portable hard drive, then COPY (don't move) all your documents, photos, music etc. on to it.
You can crate any folder names you like on the portable hard drive, so for your photos create a folder called MyPhotos (or whatever) for your music create folder MyMusic (or whatever) and so on.
Then use drag and drop or copy and paste to copy the files from your laptop to the portable hard drive. Now you have them safely backed up.
Now reverse the process, copying everything from your portable drive to your new laptop. You will have to manually put them in the correct folder (MyDocuments, MyPhotos, MyMusic etc).
If you have never done this sort of data moving before then get someone to help you (or do it for you).
While the process is fairly easy, if you do it wrong you could accidently lose or delete some (or all) of your files.