Bitpay and coinpayments are you best bets, unless you can somehow build payment infrustructure yourself which from your post you're probably not willing to.
Although you have to be warned, Bitpay doesn't necessarily have the best reputation around here in terms of their reliability so you really need to take their claims with a grain of salt in mind.
Quite contradicting. First BitPay is one of OP's best bets, then you warn him that they don't have a good reputation.
![Roll Eyes](https://bitcointalk.org/Smileys/default/rolleyes.gif)
Another point of importance is that BitPay doesn't allow anyone to accept Bitcoin without KYC. Most people looking to accept Bitcoin on their site aren't willing to go through such requirements, and that's perfectly understandable.
In case OP isn't interested in BTCPay,
Coingate accepts Lightning payments and a variety of altcoins. They do not require KYC to accept crypto, but do require KYC to have the crypto be converted to fiat and sent to your bank account. If you just stick to accepting crypto you'll be fine. Coingate offers free Bitcoin withdrawals too, which is pretty neat.