The one of my main concerns is: how safe is it to accept cryptos as payment on a website?

Yeah, that will be the next thing you should do, there are lots of payment gateways available but I'll naming a few including btcpayserver, blockonomics, coinpayments, and bitpay.
But I'll suggest to use btcpayserver if you want more control of your funds without paying % every sales you get, without kyc, and no more account lockup, though this cost you a bit developing such gateway since your the one who will host it and/or will hire a person to do it for you if don't have knowledge in programming.
While other gateways need 0.5-3% charge every sale you made, need kyc, and sometimes wait a bit longer til your funds get withdraw. Though you still need to hire a developer to do the work.