How to install apps from iTunes "Wirelessly"?

Turn on Automatic Downloads for iTunes Store, App Store, and iBooks Store purchases - Apple Support

Sync your iPhone, iPad and iPod touch with iTunes using Wi-Fi - https://support.apple.com/HT203075

I think you are going to have to do it in two steps unless you get the item directly on the phone.

You only have to connect by cable the first time you sync wirelessly, but I think it will still be two steps, get the item then sync it.

My recommendation: First, disconnect the iPhone from your computer. If you're going wireless, you kind of have to throw out the wire (loosely speaking).

Now open the App Store app (on the phone), log into your iTunes account, and download the apps directly.

When you look up an app you already own, it will show the cloud-with-down-arrow symbol. New apps, of course, will show the usual Buy or Get buttons.

Once the apps are on your iPhone, from now on they will be updated automatically, if you have that option turned on in Settings > iTunes & App Stores.

Basically, this process cuts iTunes on your computer out of the loop, unless you still use it for backup. (My advice is to cut the cord completely, back up to iCloud, and use the wire only for charging.)