But can I download Wordpress onto my computer, design the site offline if I want to, then FTP the files to my host?
Yes, you can develop offline with Wordpress. You can use InstantWP that will run on Windows. However, if this is your first time to use Wordpress I would highly recommend using it online. You can still FTP files up to the server of course.
WordPress requires a database which is not something you can upload/update via ftp. Easiest way to build a WordPress site on your computer and upload it is using a plugin like Duplicator or All In One Migration.
https://wordpress.org/plugins/duplicator/
https://wordpress.org/plugins/all-in-one-wp-migration/
Easiest way to install wordpress locally is to install xaamp and then the wordpress addon.
https://www.apachefriends.org/download.html
https://www.apachefriends.org/add-ons.html