Hi curlyhead23,
Welcome to the Apple Support Communities!
I understand that you have been syncing your iPad with your MacBook Pro and now have a new iMac that you would like to sync with. When you attempt to sync, you are met with an alert that the content on your iPad will be erased when it syncs with your new iMac.
This alert is in place because iOS devices can only sync to one computer’s iTunes library at a time without changing the data that is on the device. Essentially what is happening during a sync is the device wants to match what is in that computer’s iTunes library. This is why the content on the device gets erased and replaced with the content that is in the computer’s iTunes library.
That being said, there may still be a solution where you don’t lose any content if you sync with your iMac.
Because your main concern is app data, I will start with an explanation on what may happen when you sync and how to proceed. The first attached article below explains the types of in-app purchases, consumable or non-consumable.
Make in-app purchases - Apple Support
I know some of your concern is around the progress and time you have put in to some of these applications. The next attached article not only explains how to restore non-consumable in-app purchases, but explains how to contact the developer of applications from the App Store. As far as your progress in the apps and how that is saved, I would suggest contacting the developer prior to erasing the application from your device to ensure you will be able to recover that progress when the app is installed fresh.
If you don’t see your in-app purchases - Apple Support
If you would like to continue and sync with your iMac, I would first recommend downloading your entire purchase history to your iMac before connecting your iPad. The attached article below will explain the process to download all of your purchased music, movies, TV shows, music videos, apps, and books to the iTunes library on your computer.
Download past purchases from iTunes - Apple Support
If you do not use Apple Music or iTunes Match and some of the music content in your MacBook Pro’s library came from CDs, I would suggest using Home Sharing to move that content to your new iMac’s iTunes library.
iTunes 12 for Mac: Use Home Sharing to import items from another iTunes library
If you are not already using iCloud to sync Contacts, Calendars, etc. I would suggest doing so. This will make sure all of your data is safe and will not be erased when performing the sync to iTunes.
Apple - iCloud - Learn how to set up iCloud on all your devices.
The next content I would like to make sure is safe is your Photos. If you do not use iCloud Photo Library, please make sure to import all of your pictures to your computer using the attached article below.
Import photos and videos from your iPhone, iPad, or iPod touch to your Mac or Windows PC - Apple Support
If you are using iCloud Photo Library, please log into the iCloud website to verify all of your pictures and videos are safely stored on iCloud.
iCloud Photo Library FAQ - Apple Support
If all of the content on your iPad currently was purchased from iTunes, once everything is downloaded to your iTunes library as described in the above two links, you can sync your iPad to the computer. This will still erase the content from the iPad, but it will essentially replace it with the same information from the computer.
Best regards