Migration Asst

Another possible solution is to put your old Mac in Target Disk Mode , access it like an external HD from your new Mac and copy the files you want over.

However, any 3rd party apps that you want will have to be re-installed and their preferences set.

If you do what rakefmann87 suggests all settings will be restored as they were on the old Mac. A much easier solution.

Also, if you have any "cleaning", "optimizing", "speed-up", anti-virus or VPN apps on your old Mac, uninstall them before migrating. They are totally unnecessary and can, and most ofter will, compromise system and application performance.

You likely did not use Migration Assistant by following the steps outlined in Setup Assistant and Migration Assistant. If you follow this process (I'd start over with a fresh system on the new Mac) then you can migrate quickly and easily then go back over what you do not want to keep and put that in the Trash and empty the Trash.

Copy and Paste each file, that is your only option. Copy them to an external HD or a Flash Drive and paste them to the new computer. Migration Assistant is an all or nothing proposition.

You can try that and do file sharing, however copying and pasting would be faster and easier. Any reason you don't want to use Migration Assistant?