Using blockchain to store transactions, have transactions through blockchain

We are developing a website that would require a payment to go through at a point, or an agreement through a contract a long with the payment, was looking to integrate blockchain into the website, where the payments would be secure and be stored through that blockchain, but we are not sure whether its best to use a private blockchain and integrate it, or use Ethereum network for the smart contracts, but then for the transactions maybe through a token?

Would love some input on this.