Options I'd be looking at:
- Remotely share folders over a network and transfer
- Depending on how much data (and if you're ok with it) utilise onedrive to remotely back up required folders - obviously speed of internet is a factor here.
- Use the external drives to backup everything and then transfer over. A backup of important data isn't a bad idea anyway.
- Grab an external usb caddy for the old pc drive, take it out of old pc, stick in caddy then transfer over.
The external USB drive is likely the easiest option and a good way to 'clean out the junk' as you go, plus you get a secondary backup at the end of it on the external drive(s).
I'd also consider if you don't already do this to have a second drive (assuming case can take second drive) for your 'data storage' so it's not on the same drive as your OS, makes life a lot easier if you ever need to reinstall windows (disconnect drive, reinstall, reconnect, re-link folders to username)