If you mean the input field itself (as a visible element) then the answer is none of them, you don't need to add it since the whole row will be selectable, therefore adding a redundant input element will cause some non needed friction.
If you mean the form element disguised as a clickable row (which is a very common way of doing this), then as you say, it should be a radio button, because you can select only one item at a time. Otherwise, if you use checkboxes, you'd be allowing multiple selections.
However, keep in mind that this is not the only way to do it, and making the row active on click should be enough. Since you click and fire, additional elements are redundant and not needed at all, and users will discover the affordance with the first interaction