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The biggest issue is how to receive on-line payments and these days there a number of ways to do this. Several companies now exist to provide the processing required to take on-line payments, some are free to use, some have a membership fee, they will all have some sort of transaction fee. If they are any good however, they will provide a way of integrating seamlessly with your site and fortunately, most of them do. You may be familiar with some of the names, PayPal, WorldPay, NoChex are among the most popular. As you may expect, there are pros and cons with each of them, so it's helpful to have someone to talk to and help decide which is the best for you.
You could even do what some clients have done and avoid them altogether. You do need to be trading already and have some form of bank account and payment processing already in place. Then you just receive orders from your site, usually via email, call the customer yourself and take the payment over the phone, in the same way you may do already. Several companies use this approach and has the advantage of avoiding membership and online transaction processing fees, which can quickly exceed the cost of a phone call. Then if you find that business is going well and it is the right time to fully integrate your store, you can make the necessary move. There is no need to spend money if you don't have to.