You can use one of VerSign's products, or WorldPay. WorldPay is deisnged to take currency from all over and convert it into any bank account and its currency.
For WorldPay, they are effectively the card processing unit and the Merchant Account in one and then they feed into your bank account, which can be anywhere and any type.
The other products, such as things that VeriSign use, will process the cards, and then that data has to go into a Merchant Account, and that needs to then get transfered to your bank account (and not all bank accounts will talk to Merchant Accounts).
It is far more complicated that one likely initially thinks.
If you actually want to process the cards yourself, then you likely need a POS terminal (point of sale) - which is what they have in physical stores.
But depending on what you are selling, if you do that online, people aren't likely to trust it.
You want real time processing of the credit card over a secure connection so that ideally you don't have their information and instead just process and take the money for the transaction.
Also, it depends on what your business it - the companies that do this processing are very picky and frequently won't accept your business unless they are 100% sure nothing about it is sketchy.
Those that will process and care less about the sketchiness of it, will charge way more and you can't necessarily trust them (things like porn and gambling have to host on offshore servers and go through special offshore bank processing).
In the end, I'm trying to say that it is more complicated than you likely think.
PayPal sucks bad if you are doing illegal things, or even grey area stuff.
If you have 100% legit business (ie selling T-Shirts or something), they aren't much of an issue.