You can back up steam game data via steam client and then transfer those files to new PC and restore them there.
I do this so i don't have to redownload 1000s of GB
But for the rest, you will have to reinstall so make sure you have all your licenses backed up via Belarc Advisor.
It depends on the files you want to copy. Pictures, videos and documents will be fine, but files related to programs, such as Microsoft Office or Steam, can't be done. The reason is because programs contain registry keys, which the new hard drive won't have.
You can consider using CloneZilla to image the current drive and restore it to the new one. The only downside is that the image may take up a significant amount of disk space. As the drive will be cloned, you'll also be taking problems with you, so error messages or drive fragmentation will remain.