Is there a simple way to transport all of my contacts from my iPhone into my new iPad, can I just plug-in on these little cords from my phone to my iPad and hit send or something

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

https://support.apple.com/en-us/HT201269

Basically, presuming you have the same apple ID for each device, turn on iCloud syncing for contacts on both of them and the data should move over.

The simple answer is Yes.

On iPhone:

Make sure your iPhone's

Settings > [your name] > iCloud > Contacts : is ON (green)

Check using your computer browser if the contacts are on iCloud

https://www.icloud.com/#contacts

On iPad:

Sign in with the same Apple ID & password when setting iPad up.

Your contacts should automatically sync.