Trying to move data from my old iPad to the new one but the installation process spins and never completes. I've updated software, I'm sure they're both on the same wifi, etc. What am I doing wrong?

These support pages should get you started with setup of your new iPad - and the methods of transferring your data from old to new iPad:

Set up your iPhone, iPad or iPod touch – Apple Support

Transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch - Apple Support

Use Quick Start to transfer data to a new iPhone, iPad or iPod touch – Apple Support

If the donor iPad, from which you are transferring your data precedes iOS12.4, QuickStart will not be available.

“Transfer” is rather a misnomer. In reality, your data and setup is merely cloned to the new device. Nothing is moved or removed from the original device.

An alternative is to restore either an iCloud or iTunes backup to the new device:

How to back up your iPhone, iPad and iPod touch – Apple Support

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

Apps are not directly transferred between devices. For Apps, the transfer process creates a record of the Apps that are installed on the donor iPad - and it is this record of installed Apps that is transferred to the target (new) device. For Apps that are still available for download from the App Store, the corresponding Apps are automatically downloaded and installed from the App Store.

Not all Apps will, necessarily, continue to be available. Apps may have been removed or retired from the App Store by the respective App Developer. Some Apps may have been abandoned - and may not be compatible with the new device. Where a compatible App is not available, you’ll not be able to transfer/install the App.