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