Is their a database that can track accounts and also take credit card payments?

Most member management systems will allow for this.

What type of organization is this? There are programs out there that are customized for different types of groups.

For example I used to be the treasurer of our chamber and we used a program called Chamber Master that allowed us to collect dues, collect fees for events, communications, send out renewals, collect sponsorships, etc.

You could also go very cheap and use google forms with an integration to a square account to collect payments.

Quickbooks online. I'm sure there are better ones specifically for membership organizations.

Just set each member up as a customer/client. Set up items to be sold and then create invoices for each member as needed. might take a little bit to set up on the front end but should be simple as its just tracking cash based transactions.

Not sure if stripe or square allows for segregating members though.

You can absolutely setup to take and receive payments through QuickBooks. I owned a pool cleaning company, and processed CC’s all the time.

Customers were on AutoPay, where QB stores/encrypts their CC. Or, they could pay through auto recurring invoice, using a link from the auto-generated email. Some old customers even had auto bank drafts setup.