I've got a reliable wifi network but I need good backup facility recommendations please

Connect separate hard drives by USB to each computer and backup to them.

Backup Software

Using Time Machine is very easy, and all the tools you need come with OS X. If you later need help with Time Machine then I highly recommend a visit to Pondini's Time Machine FAQ for help with Time Machine. This is an extensive site with most everything you may need for using Time Machine. You will not find a better resource for Time Machine of OS X in one location. Due to the passing of James Pondini the site is no longer being updated. Therefore, some of the information may be outdated.

As an alternative, you can use any third-party backup utility your prefer. They all create straight file backups meaning you can restore individual files manually if you want by drag and drop copy.

Recommended Backup Software

1. Carbon Copy Cloner
2. Get Backup
3. Deja Vu
4. SuperDuper!

Visit The XLab FAQs and read the FAQ on backup and restore. Also, read How to Back Up and Restore Your Files.

Try the following to reformat your non-working drive.

Drive Partition and Format - El Capitan or Later

1. Open Disk Utility in the Utilities' folder.
2. After Disk Utility loads select the drive (out-dented entry) from the side list.
3. Click on the Erase tab in the Disk Utility toolbar. A panel should drop down.
4. In the drop down panel set the Partition scheme to GUID. Set the Format type to Mac OS Extended (Journaled.)
5. Click on the Apply button and click on the Done button when it is activated.
6. Quit Disk Utility.

Just thought with the AirPort I could do both in the same place

You can, but I think most folks would consider it a waste of money to buy a product if you don't even intend to use a feature that represents half to two-thirds of the cost of the device.

But, you may disagree with that reasoning. It's your call.

I need a reliable back up system

That would NOT be time machine.

Carbon Copy Cloner is reliable.. much more so than TM.

You need a target.. that would NOT be a Time Capsule..

What about a Synology NAS? Much more expensive though.. but long term is excellent file server and storage for backups.

Plug the disk into USB port.. can you see it?? (in disk utility or at least in System Info as connected to the USB port).

If not.. get a powered hub and try again..

It will depend on if the Toshiba disk is self powered or not.. And the exact model of your Macs.. and which port you are plugging the disk into.

How old is the Toshiba disk? If it is a small self-powered model.. you are probably going to do better with a 3.5" desktop USB drive.. in terms of long life.. Or buy a more expensive model self-powered drive.. like the LaCie.

Looking at AirPorts but I don't need the wifi facility.

Pretty simple answer here, based on your information.

One-half to two-thirds of the cost of an AirPort Time Capsule is tied up in the wireless router, so if you don't need the WiFi facility, you probably don't need an AirPort Time Capsule.

So, as far as a potential Apple solution, we don't really have anything for you that we could recommend.

Kappy has the simplest, most reliable and least expensive solution for you.

If you are interested in a significantly more expensive solution, you might want to take a look at a NAS, something from Synology or QNAP.

As far as your Toshiba external drive, you might want to contact Toshiba support on that product.