I think it is expensive for home users

I'm not buying it. 2015 will do.

Here's what I use...it works great AND it's FREE!

http://www.disk-partition.com/

Best thing about the release of a new version is that soon afterwards, the old version pops up for sale a lot cheaper.
 
Plenty of brand new copies of ATI 2015 all over the web starting around $35.  I was one who used a free utility, but have finally jumped on the Acronis bandwagon -- just ordered boxed ATI 2015 bundled with Disk Director 12 for $35 (free shipping).
 
Additionally, once registered, it's eligible for a free upgrade to the new version! 

Acronis screwed up too many times and they lost me...

Aeomi has been flawless...and FREE..which is even better..

I had the 2012 version and just updated to 2016. I had found 2012 to be clunky but the new version seems to run smoother and the interface is better. Ran my first full system backup in about 30 minutes.

I have been using ti 2015 for some time and never an issue with it. Works flawlessly. Just updated to ti 2016 and it seems fine also, tested it out with creating and restoring, cloning, all worked fine.

Is the backup to DVD or would I have to purchase a separate external HD?

Given the size of modern hard disks, backing up a drive to optical media wouldn't be practical. An external drive would be cheaper and faster.

Yup external HDD or NAS are your best options.