If you want full control over the payment process to your website you should go for a self-hosted payment processor but note that it would cost you maybe a bit more for hosting and developing if you will hire a developer to do the work, a small business might get hard to maintain those requirements for hosting.

While there are many hosted bitcoin payment processors which give you easier setup, mostly 1-2% charge in every transaction made but will give you less control over your money, especially some requires kyc, btw I recommend Blockonomics.