I'm no developer. I purchased Magento in 2015 paid a website editor to develop the web page which is good to a degree and works for sales via Paypal. I'm looking to build on selling via Ebay. Looking at the back end there has been no upgrades at all since 2015. Is there a recommended version I could upgrade to that takes into consideration all the critical and major alerts since then and a secure version to add extensions to for Ebay selling? I'm not sure what is included in the original purchase price and what I'm able to upgrade to without further purchase. Thank you in advance.
For selling via Ebay you will need an extension. I'm not familiar with that but, you might want to check some of the extensions that are available. I found this one for example: https://www.magentocommerce.com/magento-connect/ebay-magento-integration-marketplace-connect-by-codi...
About the upgrades. It's a bad thing that your installation hasn't been upgraded since 2015. There have been a lot of critical security fixes lately. I'd always go for the latest version of Magento, which is 126.96.36.199 at this moment. You can just download this version, but you don't want to upload this to your server and hope it works. If possible I'd suggest to make a copy of your webshop (on your local machine or for example on a subdomain) and upload the latest version there. Make sure you use a copy of the database as well, otherwise you'll have the testing environment using your live database.
When the upgraded version is ready, you should start testing both the frontend and backend of Magento. On the frontend, check if you can place an order, register an account, etc. And in the backend check if you can edit products, process orders, etc.
When all that works and the shop still looks good, you can copy the upgraded version to your live site.
So that makes Magento up-to-date, but what about the extensions. When Magento hasn't been upgraded, your third party extensions might also be outdated. So you might want consider upgrading these extensions as well. You can get a list of installed extensions by going to your Magento backend and then to System > Configurations > Advanced > Advanced. For upgrading extensions, I'd do the same "ritual" as I described for the upgrade of Magento itself, best might even be to not put it on live before you upgraded everything.
And then your done! For now, because Magento will keep updating Magento with security fixes and extensions developers will keep updating their extensions.
If you think the above is a bit to technical, you might want to consider asking a local Magento agency to update (and maybe maintain) your webshop for you. Security is really important, since you don't want hackers to capture your customers personal information or credit card information.
Good luck upgrading! I hope my answer helps you out.
Everything that Arjen said is absolutely correct, but I'd recommend caution in trying to make any of these changes yourself. Unless you are quite technical, and honestly really only if you have experience with Magento development, I would advise against trying to make version changes/updates yourself.
Although merchants can often be hesitant to invest additional funds, it's money well spent to ensure your store is running properly (and quickly) and you're not exposed to security risks.
I'd recommend finding a solutions partner who can not only help with the updates to your website, but also has experience in helping merchants expand to marketplaces. While it may seem as simple as just installing an extension to send your products up to eBay (and Amazon, Rakuten, etc), it's important to approach this strategically in order to be successful.
I have to agree with Jared on this one, finding a solution partner in your area can be a smart move here. Spending money to make your webshop secure and functional again will, in the long term, always be cheaper then having a hacked webshop, issues with credit card companies because of PCI compliance stuff, etc.
On this page you can find a solution partner near you: https://magento.com/partners/portal/directory/?partner_type=1.