Changing jobs shortly and my current works phone is a Galaxy S3.

My new works phone will be an identical phone.

Is there a simple and quick way to simply transfer all my contacts and apps from my current phone to a new phone?

Sync with your Google account and it should Just Work.

It won’t transfer data / settings though, so you’ll need to back that up separately. Titanium Backup is widely regarded (though I find it a bit awkward personally).