Of these options, the product whose demand will be most inelastic is likely to be toothpaste. The other possibility is gasoline, but the demand for toothpaste will be more inelastic, particularly in the long term. The other choices will all have relatively elastic demand.
One major determinant of elasticity is the availability of substitute goods. If there is something else that you can buy instead of a given good, you will be likely to switch to it if the price of the given good rises too much. For the bottled water, the fresh green beans, and the cookie dough ice cream, there are plenty of substitutes. You could drink tap water or juice or soda. You could buy canned green beans or you could buy some other vegetable. There are any number of other flavors of ice cream. But for toothpaste and gas, there are no good substitutes. (In the long term, you can do more to cut your need for gas: you can buy a car that uses less gas; you can change your lifestyle to do less driving. You can’t very well cut your need for toothpaste.)
Another determinant is the urgency of the need. The need for toothpaste and gas is typically rather urgent. You can’t put them off. For the others (with the possible exception of bottled water), the need is not very urgent.
Finally, there is the issue of how much you spend on a given item. This is one thing that makes toothpaste’s demand less elastic. We spend much less on toothpaste than on gas. Therefore, we don’t care so much if its price goes up. It won’t have much of an impact on our overall budget. An increase in the price of gas will.
For these reasons, toothpaste and gas will have relatively inelastic demand, but the demand for toothpaste will be more inelastic than the demand for gas.