Transferring Contacts, Photos, etc manually from old iPad to new

The reason I want to do this as opposed to just backing up old to ITunes and restoring to new is I’m afraid I will be transferring old problems as well. I have problems with built in key pad on many occasions not typing c, m, n and v letters. I tried all solutions found on line with nothing working. Last option was to reset iPad and did not want to do that. I’m pretty sure it is one of my apps causing the problem. I want to manually sync between the old and new iPads just IMessages, Contacts, Photos, Mail etc that aren’t causing any problems and then just install my apps one at a time and making sure each one will not cause the typing problem.

Not quite sure how to do this, any advice appreciated, thanks!