We use Bank of America. They offer online payroll for $15/month. Free if you pay with direct deposit and all of your employees have BofA accounts. They will prepare and file fedaral and state tax forms and payments as well. That's a very good deal.
We use Quickbooks online (QBOE). Clunky interface. MSIE only. But it's a webapp (don't worry about backups).
We use PayPal for credit cards. They are not "unprofessional" and their API is simpler than any bank or merchant company that I know of.
For the least hassle, PayPal's got a few options for payment. PayPal IPN can handle monthly subscriptions, and the service charges are not bad. You need to be diligent about moving the money out of the account, and about handling customer service problems.
Quickbooks is the default, but you can just keep a shoebox for your records and give it to your accountant every so often. You need a finance pro anyway, and if you don't have a founder who is an expert, outsource. You can't afford to screw that up.
I use freshbooks for all of my invoicing etc. I couldn't be more happier with it. They will even post your invoices, estimates etc. You can also take payment for your invoices online with them.
Just get a no-fee business checking account at a convenient bank with a debit card, once you are making or spending a lot of money you can shop around for something that suits you better.
When I was a student, I had a big problems with Fifth Third. Really stupid stuff like "unresolvable computer errors." I had to close an account and re-open it to solve the problem.
Needless to say, I didn't keep that new account open for long.
We use Quickbooks online (QBOE). Clunky interface. MSIE only. But it's a webapp (don't worry about backups).
We use PayPal for credit cards. They are not "unprofessional" and their API is simpler than any bank or merchant company that I know of.