If your hosting providers has installed Softaculous, you can get into the auto-installer and test the dozen of e-commerce and shopping cart solutions available inside this. All those scripts are some of the best shopping carts you can install, and all of them are free.
Judging by the inquiry I hope I'm safe to assume that you are a novice user and this will be the first time you build an online shop. So I think that just choosing any cart won't do you any good, as there are some, like Magento for example, that will require more effort and knowledge from your side. This is why its best to start with something easy, yet functional. My personal choice would be PrestaShop as its learning curve is not steep, works quite fine, looks good, has many free modules and themes and of course - a great community to back you up if you are in a dead end. Alternatively you can try ZenCart if you have a better feeling of it