Hello, Diane. The word you want is "migrate" and yes, you can do that as long as the old drive works. When you get the new one, it will come from the factory with the operating system installed. When you first boot it up, it will go through a welcome process and at some point ask if you want to migrate old data from an old machine. At that point, say yes to that, connect the two and follow the directions. At the end, all of your files will have been migrated to the new system, applications that will run on the new will have been moved over and an account created for you that is exactly like the account (same password, even) on the old machine. Now, some applications don't migrate as well because of how the company handles licensing, so for them you may need to uninstall from the old to install to the new, or re-register with the developer. Adobe products (Photoshop, etc) and Microsoft products (Office) are two that I can speak of from experience. Adobe has to be unregistered and reregistered, Office the same.
As for clean up, by all means, if there is stuff you do not want to have on the new, get rid of it before the migration. And of course, make lots of backups that you test before diving in.
One suggestion. Get the new system BEFORE the old one dies completely because you want to be able to migrate. If the old one dies, you'll need to remove the drive from the old, put it in an external enclosure and migrate files from there. That will work, but if the old one dies in the middle of a write to the drive, you might lose the drive integrity. So do the move before you are staring at a dead machine and reduce the risk.
Now, it is also possible to migrate from a backup, so if you make them frequently enough that if the old one dies JUST BEFORE the next backup was do and you lose the maximum number of changes since the last backup, you can live with it, you should be alright. Otherwise, speed up the frequency of the backups so that you can live with that loss. Murphy's law will have your old system die in the middle of a new backup, forcing you all the way back to the last one and if there are things you've done that you want, they are gone.
Hope that helps in the planning process.