Disk size of a bootable external HDD?

Basically you need enough space so that you can copy the entire Mac contents using Carbon Cloner or similar. It might be 170GB now, but it will grow...I'd go with a 500GB drive to be safe. Plenty around these days and cheap too.

 

What bus are you using? USB, FW, T/Bolt? You can in theory partition that drive and create a bootable ML copy, or clone the whole Mac ( a better option really) but It's a rule of mine that I leave TM on it's own disk without any other partitions...I use a Time Capsule which has a lot of free space, but I use it solely to backup my Imac and rMBP.

Your call...but drives are so cheap now that buying a dedicated unit for your copy might be a better idea.

 

If you have an iMac with a 320gb drive inside, and if about 170gb is used….

You could get away with a partition of, say, 180gb or so -- but that doesn't leave room for "future growth" on your internal drive. Not the best solution.

You'd probably do better by creating a backup partition of 300gb or so. Thus your backup clone can "grow" as your internal drive does.

IMPORTANT:
If you decide to create a partition on an existing drive to become your backup clone, I STRONGLY SUGGEST that you make it the "first" partition on the drive. If you maintain a Time Machine backup, put them on the "second" partition (or third, etc.). Keep the partitions that you want to be bootable "towards the top". Things just seem to work a little better that way.

You can use either CarbonCopyCloner or SuperDuper to create your clones.

Don't be intimidated by any of this. Creating that bootable backup could prove to be a lifesaver if you ever have an "I can't boot" situation with your internal drive. Just connect the backup, and you'll be booted and running again in the matter of a minute or two.