How do I transfer data from a 550 GB iMac to a new iMac with 256 or 512GB storage?

I would advise against buying any new Mac with only 256 GB of storage.

If you have a lot of disk space taken up by things like music, movies, TV shows, photos, and videos, you could consider putting your Music, TV, and/or Photos libraries on an external SSD. That might let you get away with having just a 512 GB internal SSD. But you'll have to do more work to get everything migrated.

A no current iMac have storage that can be upgraded after the computer starts down the assembly line, I recommend buying one with 2X the storage for your current leads. SSD storage doe not do well when nearly full.

YOU don’t you guy a MM with 1tb of storage..You cannot put 1 gallon of milk into a 1 cup container.

What do I need to run a new iMac with 256 or 512gb storage built in?

You need to reduce the amount of storage you are using by at least 50% — and that would be for the 512 GB model.

I strongly recommend not buying any Mac with less than 2x the capacity of what you have now.

If you can find a way to reduce your present storage needs to 256 GB, then a 512 GB iMac will be adequate... provided your storage needs will never increase over its expected useful life. That can be on the order of seven years or more. Only you can estimate how much storage you expect to be using in 2032.

A 1TB iMac would work. Or, you just don't copy everything over.

You need to be selective about what you are going to transfer to the new Mac.

Like the old saying goes... you can't fit 5 gallons of dirt into a 1 gallon bucket.

What you should do is simply purchase a Mac mini with a 1TB SSD. You cannot put 1 gallon of water into a 1 cup container. Yes, I know it is more money however it is the correct method to take unless you are highly technical!

I have since ordered a new 1tb iMac directly from Apple.

Excellent decision.

A VERY wise decision, enjoy your new Mac mini!