I’m not familiar with website setup but hopefully one of these could be the right solution for you.

1) BTCPay server

-must be self-hosted

-maximum decentralization, private payments direct to your wallet

-probably most difficult to setup

2) Strike

-centralized but free withdrawal to cold storage

-easy integration and use

-no server management

-settles in USD

3) Open Node (I have no personal experience but heard good things)

-subscription

-settles in BTC or USD

-ease of use