Best way to backup my Mac? Use a PC at work. Have a 2TB portable HD. – Info Mac

I have a Seagate backup plus slim.

Do I need to format it? Exfat? Will that let me run time machine? Is time machine best or just copy files over? Do I need to partition?

I need to use this and use files both at work and at home. Also I use cloud services – does time machine back those up as well?