XBox 360 Arcade question

Okay I have the fat Xbox 360 arcade 20gb and want to know can I used USB 1TB external hard drive for it or should upgrade my Xbox 360 to Xbox 360 Slim or Xbox 360 E lite.

I have Xbox one

I use an external 500GB HDD with my Arcade 360, runs fine, you can move any game installs to it and directly save to it too.