Options? Fully manually as you’re seemingly headed toward here, or using Migration Assistant.
With the latter, you’ll get to select different subsections of the contents of the old system for transfer, but this isn’t an incremental process that can be re-visited. It’s a one-shot transfer. And it’s not very granular, as BDAqua mentions. Select what you generally want to transfer over, and it’ll get hauled over. Or select it all.
After that Migration Assistant transfer, you’ll either be picking bits out of your backups if you’ve transferred less than everything, or cleaning up what was transferred.
If your new Mac has equivalent or greater storage capacity, I’d haul it all over, then clean up. Mixing the transfer and the clean-up seems like incrementally adding more work. And a good way to lose files.
Have backups. You’re headed for High Sierra, or Mojave. If this is a new Mac, you’ll get Mojave for a little while more, then (real soon) Catalina. Have backups. And check your key apps. And check that your printer and scanner vendors have drivers available. Did I mention having backups?