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Your selection of a lead screw will be based on the parameters of your design such as. How far do you need for it to move back and forth? How much space might be taken up by a carriage. What precision will you need in your motion? How much force is this lead screw expected to encounter? How fast does the lead screw motion need to be? How are you planning to drive the screw? How will it be, or can it be supported at the ends? etc.

Many commercial lead screws are more precise and powerful than needed for many FIRST applications so you may be able to get by with a lower cost/grade of lead screw depending on your design. A low carbon steel screw with a plastic nut in 1/2 inch diameter or even smaller should work for a wide variety of applications. But if this is intended to do serious work such as lifting the robot, then you better research the answers to the above questions carefully before selecting a lead screw.