If, as you say, your current data load is less than 200 GB and you want to migrate that to the 256 GB startup drive of a Mac mini, then yes, Migration Assistant should be able to do the job and move that data to a low capacity Mac.
However, I would strongly suggest that you don't accept the basic 256 GB drive of the Mac mini, but bump it up to at least 512 GB. One reason being that for the sake of the proper operation of the OS it is recommended that one always maintain a minimum free space on the startup drive of 10%-15% of the total drive capacity. For a 256 GB drive, that means at minimum keeping 25 GB free, always.
While macOS on a Mac out of the box may only occupy 30 GB (+/-), adding your 200 GB of personal data will exceed the suggested allowance of free space. Every day we see here in the community complaints of slow Macs and excessive System data sizes that compromise Mac performance. Most often these complaints come from users who have skimped on the storage and bought only the minimum 256 GB Mac.
No veteran user will advocate buying a 256 GB Mac in todays computer environment. Do yourself a favor and future-proof your Mac at least by a little bit and start with 512 GB of storage at minimum.
I understand that you keep your data on an external drive, but your current situation suggests you're already running your current Mac at the edge of its suggested storage limits. Since the internal storage of the Mac can't be modified after purchase, you'll be stuck with whatever you buy for the life of that Mac. Apps and OSs are only getting larger in size.
