Have a look at ccbill and epoch.
Try to get your own merchant account by all means if you can.
As for banks, any mid sized or large bank that will take your business will do, the bank itself is not that critical (other than that it would be nice if they stayed in business).
FirstData is a gateway, not an IPSP, and it would take you a lot of time, money and certification fees to get connected to them. Having an IPSP in between will save you a ton of heachaches, as well as lower your profile as a target. The price of hosting for servers that are certified is also much higher than for run-of-the-mill webservers because you have to ensure that physical security of your server is warranted at all times, and most hosting facilities can not do that (they have customers visiting the server rooms and unless you have your own locked rack people will have access).
The downside is that you will not have the customer card info/cvv information so if you ever have to switch IPSPs you are basically starting from scratch.
In practice this is only a problem when an IPSP falls over, but as the IBill and DMR history shows this occasionally does happen and it takes thousands of merchants down with them.
One more reason to get that merchant account of your own, at least like that you'll get your money if the something bad happens.
I use vxsbill myself, it is run by friends of mine, but the downsides for people from the US (which I assume applies to you) is that you need a dutch presence to make use of them and the application fees are steep.
The upside is that they are rock solid (or at least have been to date), each and every one of their customers has a separate merchant account, so a misstep by one customer does not affect the others.
Without segregated merchant accounts that is a very real risk.