I would personally look into using crypto currency. It's faster than every other solution out there. It's cheaper than every other solution out there. It also has a bright future if you hold it instead of cashing it immediately.
Bitcoin is NOT a privacy coin. It doesn't do anything to hide transactions, it has a public blockchain and does nothing to obfuscate your IP address. That said, if your goal is only to accept payments from people and have those people not be able to identify you, bitcoin and many other currencies are fine.
The way people get caught doing bad things with with bitcoin is
- not obfuscating their IP address when transmitting
- and linking their wallet address to a public deanonymized profile.
So if you were to create a new bitcoin address and just use that address on your business site, it'd be pretty anonymous from average users. The government would be able to find you though. Also if you ever tie that wallet address to a public profile it's instantly deanonymized.
This is where option 2 comes. There are a few great privacy coins out there. I prefer Verge personally but there are certainly others such as Monero.
Verge obfuscates your IP address by transmitting natively over TOR or I2P. It also has stealth addressing built in natively which means that you never expose your wallet address to the world. Using public private key encryption, a unique anonymous address is generated using public keys from both the sender and receiver. This address is what's put on the blockchain and is untraceable. Only the receiver will ever be able to claim funds posted in this manner and until quantum computing becomes accessible, it is unbreakable with todays computing power.
So in summary:
Cryptocurrency is easy to use, is extremely fast and extremely cheap. It's also appreciating in value at a ridiculous rate over the last few years so it
could net you more than you originally asked if you don't cash it out immediately. That said, if you do want to cash it out, there's great solutions for that. Such as Coinbase's new merchant solution and also recently Litecoin announced LitePay. I personally have used Coinpayments in the past and it was a nice option as well.
To the OP, don't be discouraged by the downvotes. This is a legitimate answer. The people that are downvoting and not commenting why are either not in the crypto market or have a vested interest against it.
Anyone that looks at the technology though and understands that major companies, Wells Fargo, Amazon, Ebay, JP Morgan, Moneygram, Western Union, etc etc etc etc etc, are investing time and money into it, it's not going away.