Hello Clarkd52, and thanks for the question.
If you're just attempting to accept donations on your website, then there wouldn't really be a need for an eCommerce solution for your site, unless you were accepting donations for products or services that you would have visitors add to their carts.
If you were instead just providing information on the website, and just wanted to allow visitors the ability to leave you a donation. There are various services out there that allow for this type of functionality.
Google Checkout for Non-Profits which offers 100% free of charge processing if you also are accepted for Non-Profit Google Grants.
Another alternative would be PayPal for Non-Profits which offers a discount on the standard PayPal processing fee.
There are many other services like these two out there, and some searching might turn up a better alternative for your particular needs.
Now in terms of the software you'd want to use to actually create your website, depending on if you plan to have products or not, I would probably lean towards WordPress if you're just having an information website. Or use something like PrestaShop if you were planning on setting up a site with shopping carts and a checkout.
Please let us know if you had any other questions at all.
- Jacob