A lot of people use bitpay. I'm not sure of their policies with regards to "high risk businesses". A nice feature of bitpay for many merchants is that they can convert the received funds into USD and deposit to your bank account.
Also, Bitpay is a third party, and it is more in the spirit of bitcoin to accept it yourself directly.
There is a software package for directly accepting Bitcoin called
cryptowoo that has a nice feature-set and is well maintained. It is not free, but is inexpensive and does not have ongoing transaction fees. note: I am not the author of that package, but I did recently survey all the available open source packages and found cryptowoo to be a superior alternative.
If you are technically inclined, you could install cryptowoo yourself. Otherwise, you would be wise to seek the services of a professional.
also: Besides cryptowoo, it is not *that* hard to hack together a custom solution that uses bitcoind. The trickiest part is avoiding a hot-wallet situation.