how to transfer photos from Ipad to a new computer?

You can import the photos and personal videos this way.

iOS: Importing personal photos and videos from iOS devices to your ...

You can download many movies again for free using the same Apple ID that you bough them with as long as they are still available in iTunes and as long as free movie downloads are available where you live.

Downloading past purchases from the App Store ... - Support - Apple

You will have to search the net for a third party program to recover the photos sync through iTunes on your old computer. The links Demo gave will only get the photos and videos taken with the iPad's camera or save though other sources and stored in Camera Roll.

Be aware photos sync through iTunes may be a lower resolution than the original depending on the camera they were taken with. iTunes compresses higher resolution photos to suit the display on idevices to conserve storage space.

On top of your local backups I would encourage you to keep an off site copy of irreplaceable files. Either on line or I have a couple of portable USB drives I alternate between home and my mother's house.

Sync Your iOS Device with a New Computer Without Losing Data

http://www.howtogeek.com/104298/sync-your-ios-device-with-a-new-computer-without -losing-data/

Syncing to a "New" Computer or replacing a "crashed" Hard Drive

https://discussions.apple.com/docs/DOC-3141

 Cheers, Tom 😉