How could I install World of Warcraft on my new computer?

I just got a new computer and I want to install World of Warcraft on it. I already have an account, but I’m missing some of the disks. I have the codes from when I bought the game before though. I don’t have an external hard drive either. Any suggestions?
Oh alright! I saw the download PC client earlier but wasn’t exactly sure what it would download. Thanks so much!