Yes, eCart can be used to create an online store that the user can purchase using a credit card.
That functionality of power store was created using eCart.
Where you say you pick things up quickly, you *may* or may not be able to pick how to create this. Keep in mind that are a number of things you are going to have to pick up quickly though. There will be a fair bit of PHP coding involved in this, you will have to get familiar with creating a MySQL Database, and relational datbase design. You will also need to get familiar with creating complex MySQL Queries using SubQueries and Joins.
Yes, setting up PoweerCMS is a walk in the park compared to what you are trying to accomplish. With PowerCMS all the logic has been created for you, for what you are trying to do, you will need to figure out the logic and how to implement it.
If you decide to do this yourself, the best advice I can give is:
1) Don't impose a dead line. or if you do, be very realistic, you will probably need to double whatever you *think* you can accomplish it in.
2) Draw a flow chart of how you think the site should work. Then work on each piece one at a time. if you think in terms of "a leads to b" then figure out how to make "a lead to b" before moving on to the next step, it will become a lot easier.