Only one product then how much traffic do you expect?
Small VPS may be the way to go, stable platform no hardware to worry about, most hosts will allow you to upgrade the VPS package as you need more resources so you can start with the small package and then move up as you get more popular.
If you start with a dedicated then you have to take into account the running costs of the server and the admin tasks required.
Which shopping cart will depend on how you are selling the product and which payment gateway you use. Some will provide you with the cart or suggest a particular one which supports their platform.
If you are using a Third Party Processor then you will have to take into account their regulations on what you can sell and to who(geographically), fees will range around 5% plus. If you have enough volume then a merchant account with a local bank will be cheaper.
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I can say this much, you definitely aren't looking for VPN
That would be a Virtual Private Network, very handy for a list of purposes but is not an E-Commerce solution. Trigger mentions VPS, or Virtual Private Server, which might be a good start if you aren't sure how much traffic to expect.