If you are going to accept credit cards on your website and not use services like Paypal or Google Pay then you have selected the right link.
First Data seems to have a hold on this category in regards to notice or publicity. They have many partnerships established thruought the web and many link to the free merchant account links. It seems to be their business focus to concentrate on this category. It is possible there may be less expensive transaction based financial institutions available but remember we are talking about FREE so you have to consider its free to apply and get your terminal and software but you do have to pay for transactions and possibly a monthly fee. I am only considering this one even though it comes with a hitch because there are no real FREE services or products in this category and it is so important if you sell direct to the consumer. I did hear a rumor that both Walmart and Target are lobbying the goverment to change this practice of charging the Merchant some transaction fees so stay tuned this category is probably going to change.