Mobile presence is a must because close to 60% of all people use their mobile devices to shop.
If you are in the process of making a new store you can use a responsive template that will automatically give your store the right look and feel on all types of devices.
Mobile website should be always the first step because it is easier to do and it has the widest reach. Do it once and all browsers will display it.
Apps can be more sophisticated and use additional technologies available on the device such as GPS and access to contacts but they are more difficult to make
Apps in general require more work and they need to be approved (iPhone) and deployed to the app store.
Apps have a place on your phone as opposed to a browser link, which on mobile, is sometimes difficult to find.
Apps don’t have browser issues and in general they provide better performance.
If you are not a well-known store, users will not look for your app but they may still find your mobile website using a browser search engine.
Mobile apps don’t work with pay per click advertising but they can use display ads.
I hope this is enough of the differences to make your decision a bit more easy. Budget, time to deploy, your name recognition, and desired store features all need to be considered in order to answer my question in title.
