You can directly go for factor analysis. It will help you identify items which are inconsistent. It will also provide you with estimated reliability if any item is removed. You can take an informed decision based on rotated component matrix and factor loadings.
Factor analysis should be conducted to reject or select the item base on item difficulty and discrimination. Then we should go for reliability analysis with selected items only
After piloting the research tool, the first thing to do is a reliability analysis. This will help you check if the tool consistently measures what it is supposed to. Factor analysis should be done afterward to see if the questions in the tool group together as expected.