Each of the POS platforms that I looked at offered an integrated E-Commerce solution. Because Adagio was a web shop first, and has built up a pretty impressive E-Commerce environment, we aren't really interested in moving over to another solution. CounterPoint runs on a SQL Database and so we will be building integration hooks between the Adagio E-Commerce database and my retail store database to share information like customers, gift certificates an inventories. The integration is not terribly difficult or expensive, but your costs will vary dramatically based on the details of your business and what you're trying to integrate.
All of the top POS solution offer integrated, online credit card processing. You'll need to set up a separate merchant account for each location (though it can and should be with the same provider), but it's a relatively simple process. The rates are lower in-store vs. online because of reduced risk of fraud.
If you are looking to launch both in-store and online at the same time, I would DEFINITELY recommend choosing a solution that supports both sides of the business seamlessly. It will make your life a whole lot easier.
CounterPoint does this, but I probably would have worked with Celerant if I was planning to use their E-Commerce platform as well. The online tools and integration between the two sides appeared a little stronger. For what it's worth, both Teavana and Teaopia are using Celerant in-store and online.