Start with your needs. Do you need a subscription service, or just the ability for people to pay one-off? Do you need fast and easy, or robust and integrated into an uncommon business accounting software? Is the product digital download or a physical product you're shipping out of a warehouse/store?
I've worked with over a dozen of the leading ecommerce payment services, and will walk you through the best options if you set up a call where we discuss your needs.
Go with PayPal or Braintree, its your vanilla option. If you have expertise in integration, go with Stripe as well.
If your business is high risk, go with ccbill or instabill.
Also consider adding a Coinbase or BitPay account for bitcoin payments. It costs nothing to set up and is also immune to chargebacks.
This really depends on whether you already have a business checking account. Most banks partner with Authorize.net for online merchant services. If you do have a bank account contact your bank and they will be able to get you a better transaction rate than you could on your own going through Authorize.net. However, if you don't have a checking account then it depends on what level of integration you need with your online service. PayPal Payments Pro has some of the best integrations, consumer trust, and ease of use.
This is a hard question to answer without knowing exactly what application your merchant service would be interfacing with and what you would need it to do. If you want to discuss your project in further detail I would be happy to help you.
If you have a SaaS model, I would recommend Stripe. I have used it successfully for so many apps, it works well for web and mobile, and there are variety of useful and 3rd party services such as for advanced metrics, custom dashboard and so on.
