If you mean payments for when you are selling something on your site, then yea BitPay is one option(even though I hate paying through BitPay). An alternative is BTCPay[1], though I really don't know which is better. Proceed with caution as I really haven't tried implementing either on a website myself.
If you mean for donations, then you can simply add in a wallet address and a QR code somewhere on your site.
[1]
https://btcpayserver.org/Yes i need something for payment, and I also need something for recurring income.....
So member a) Pays for recurring monthly income service
or member b) wants to join for 12 months so straight out payment 1 time, anually.
or member c) Just wants to purchase from a shop, 1 time, 1 ever
Sorry, I hope I have explained myself more clear here.