How do I restore select apps and data on new iPad?

Available native transfer/restore methods are all-or-nothing; you cannot selectively restore. You can transfer everything from old to new iPad, or restore a pre-existing iCloud or iTunes backup of the old device to the new iPad - and allow the process to complete. When the process has been completed, you can then selectively delete the Apps that you don’t require; deleting the App also deletes any associated App data from the iPad.

Alternatively, you might choose to setup the new iPad manually - installing only the Apps that you choose from the App Store. You will then need to manaully transfer any App data/files that you need from the old iPad to new - using AirDrop, iCloud or external storage (e.g., ThumbDrive or similar).

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.

The alternative process is to restore either an iCloud or iTunes backup to the new device - accepting that all existing Apps that are both available and compatible with the new iPad will be automatically installed from the Apple App Store:

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

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