The biggest concern your customer will have while shopping with you is the trust factor and the level of security. It’s natural from the customer’s point of view. But from your angle, this may be an obstacle that you need to overcome.
There’s a slew of unwanted viruses and scams on the internet that may make your customer doubt you. You can eliminate this doubt by answering their questions and reassuring them by having things like social proof, secured networks for payments, and other measures that keep the integrity of your customers and your store.
Such an effort won’t only be for customers but for your business too. After all, losing a store after hours of work doesn’t make sense.