All good points of view guys, thank you all. I completely agree re: hotlinking, it's very rude to do so. That said, in my case it is allowed. All the images would be hosted. I've now spent more time researching, and here is what I've leaned so far and the resources available.
1. Hosting the images on your own server gives you control over size and optimisation
2. AMP (Accelerated Mobile Pages) and Schema and Speed (Loading times) are now very important to SEO
3. Cloudflare is awesome and as are other CDN (Content Delivery Networks) - though I've only just got started with cloudflare. Basically, using their free account, they will cache all your static content all around their networks, and those of their partners, globally. This reduces page loading dramatically. They have a nifty plugin for Wordpress too.
I'm a Linux user and discovered this useful little JPeg and PNG optimiser, there is a Mac tool here https://imageoptim.com/api
that the Linux version was created in response to.
Anyone reading this, I cannot overstate how important image optimisation for fast loading, but also with File names and filling in that ALT text - all this has a large impact on SEO - so for a few minutes work or a few lines of code to automate, or use Wordpress cause it has many features built in.
Remember, if you display a 2500 x 1500px image resized by the browser to 250 x 150px, it still has to download the 2500 x 1500px image, so use your head, mobile browsing is number #1 now, thank you Steve Jobs.
Also, use your keyword at the start of the image file name. So DF118.jpg is total rubbish. Describe the image in the file name as well as the ALT.
I've been learning a lot about SEO, it's changed so much since I last had anything to do with it. I've had to backtrack so many times to get this site right from the get go, fortunately, the next site will be a lot easier.
Original content is still king, but from a techy POV - the image thing is on the flipside of the coin.
Any other suggestions, links to things that you have used to positive affect (or negative and that which should be avoided at all costs!) then by all means, keep the thread alive (content is King after all)