If you intend to do searches directly within Prowlarr, you need to add Download Clients. Otherwise, you do not need to add them here. For searches from your Apps, the download clients configured there are used instead.
Select the download client you wish to add, and there will be a pop-up box to enter connection details. These details are similar for most clients. Some will ask for a username or password, some will ask for whether to add new downloads in a paused/start state, etc.
Client priority only matters when 2 of the same type (usenet or torrent) are added. 1 is the highest priority, and if multiple clients of the same type exist and have the same priority, Prowlarr will alternate between then.
What hit me, though, was: could one also use something like prowlarr to centrally manage my download clients as well? I could also see syncing the various things like remote drive mappings, as well.