System image installed on another partition...backup OS install?

Restoring a System Backup Image with a program such as Macrium should not take very long, say 30 minutes or so...
You will need a bootable Recovery CD for whatever Imaging program you use, such as Macrium.
When you have a good backup image(s) and a bootable recovery disc, you should never need to reinstall Window.
Learn to restore an image yourself, and then if possible, teach them "hands-on" how to restore the system.
Document it for them, step by step, and make them do an actual restore, so they learn.
If malware is the biggest problem and you have to go into BIOS to fix things because of malware, I'm not sure what to say.

What real time Anti-Virus and Anti-Malmare programs are you using?
Any decent program should update definitions automatically.
There are free (or low cost) programs such as MS Security Essentials, Avast, Malwarebytes Pro, ... that do this.

Personally I store backup images on multiple HDs, so if any one HD fails I can still recover.
One of those backup locations is a partition on my main HD.
Some people may cringe at that, but imho an external HD is as likely to fail as the main internal HD.
99.99 % of the time I recover from an image saved on a different partition on the main HD.
I'm usually restoring to remove a program I installed and don't want, or made system changes that did not work out.
If that HD fails, or malware might have infected the online image, then I use an image from an offline HD.

If you can't teach them, I understand...
I'm a senior citizen and most of the people I help are 60-90 years old.
Some of them have children/grandchildren/friends that use the PC and do who knows what.
If I'm lucky, maybe I can get an answer to what one of them might have done to cause the problem I'm called to fix.
And, I'm thousands of miles away, trying to do this using Teamviewer and talking on the phone.
I'm doing good if I can explain how and why to burn a set of recovery discs for a pre-built, and then have to get them to go to BB and buy some discs.
So, I'm not able to drive 30 miles and get hands-on the PC.
Many times I replace their Anti-Virus and/or Anti-Malware programs(s).
I recommend MSE for most people - it's simple, light weight, free...
Maybe these folks need something a little more robust such as Avast free, but that is more complicated...
MBAM pro is a lifetime license, so it is very inexpensive - $25 or less, no annual renewal fees.

Thanks for the detailed reply.

They had AVG 2012 installed but as far as I can tell wasn't scheduled to run regular scans. That's my pet peeve about some of these programs, it's not always obvious how to schedule regular scans. I don't know if AVG automatically checked for updates in their case, or whether any virus scans were run manually. Malwarebytes (free) was installed too but I don't think they ever used it. Their Java and Adobe Flash versions were ancient (2+ years old) and I suspect that's how the viruses/malware got in.

How much room would you leave in extra partitions to store the HDD images? On the primary HDD, would you do C, D, E with D being HDD image(s) and E for documents and pictures?

What size should each partition be on a 1 TB drive?

A backup image uses apx. 60% of the space used on the partition.
For me the C (OS+programs) partition uses ~40 GB, so a backup image is 20+ GB.
I like 100-120 GB for the C partition to allow for growth.

You need to see how much space they are using for their partitions.
Then decide how many backup images you want to keep, and plan space accordingly.
For data backups, imaging may not be the best solution, but it can be used.

Yea, some programs can be difficult to find all the settings and make sure they are set the way you want them.
I can't comment on AVG, I've never used it.
Avast is difficult and they like to re-design the UI every year making it more fun.
I will say Avast auto updates and scans work very well.
MSE is much simpler to set up...
MBAM Pro is also pretty easy to configure.
Might be worth considering spending a few bucks for MBAM Pro to get Real-Time protection, Auto Updates, and Scheduled scans.

No matter what, someone needs to take responsibility for periodically checking that all Updates are applied, and Security scans are clean.
2 years out of date for Java and Flash is like having a malware magnet.

I use these programs at least monthly to check for out of date programs:
Free Computer Security - Personal Software Inspector (PSI) - Secunia (I use the older Ver 2.0)
FileHippo.com Update Checker - FileHippo.com

I help some people remotely using Teamviewer and make sure their PCs are up to date and scanned.
TeamViewer - Free Remote Control, Remote Access & Online Meetings