Nick here from Shopify. First of all, congrats on joining Shopify and welcome!
You can use a credit card to make the first purchase, that should be no problem once your payment gateway is set up and working correctly. Have you set that all up yet? If not, let me know what country you're in and I can help point you in the right direction to get this sorted out.
Just to confirm, that the sale went through ok for you since, so all is good there?
I asked where you are based to show you the payment gateway options available to you, for where you're located. You can see the full list here, but also being in the USA makes you eligible for Shopify Payments too!
You also mentioned about the order not being fulfilled yet. You can see more about fulfilment with your store here.
I can take a look at the public side of your store to make sure all is well on that side if you'd like. If you want to have someone take a look at the admin and settings side, you would need to contact our support team directly as we are unable to look at account specifics in the community currently for privacy and security reasons. You would need to contact our support team here directly about this if you wanted to have someone take a closer look or to discuss it in real time!
Regarding one of your products being in violation, if you are using the Shopify Payments gateways, then it could be one of these products listed in Shopify's Acceptable Use Policy here. If you are not using Shopify Payments, then you would need to check the acceptable use policy of the gateway you are using as it could be slightly different.