The trend for radius is that it increases down and to the left

Atomic radius decreases as one moves across the periodic table from left to right, since effective nuclear charge increases and the electrons are held more tightly to the nucleus. 

Effective nuclear charge increases as one moves across a period (row) from left to right, so Cl will have a higher effective nuclear charge. Anions of an element have a lower effective nuclear charge than their parent atom, since they have more electrons than protons and feel less of a pull from the protons in the nucleus. Thus, Cl will have the highest effective nuclear charge. 

Electronegativity increases as one moves left to right across the periodic table, it also increases as one moves up the periodic table. This is because of the changes in the atomic radii of elements that occurs as one move in these directions.  Flourine is the most electronegative element because the positive charge of its nucleus exerts the strongest attractive force on it's electrons when compared to the other elements.  Conversely, the nuclei of the elements in the lower left hand side of the periodic table exert the weakest attractive force on their electrons when compared to the other elements. As one moves from left to right within the same period, one electron and one proton are added to each element.  The electrons will not be any further away from the than the previous element but there will be one more proton with which to generate attractive force on the electrons.  So the upper left hand elements have the most protons within their respective period with which to generate pull on the electrons. The electrons of these species are also the closest in proximity to the nucleii. 

Ionization energy goes up across the period and down as you go down the group. This is the energy required to remove an electron. Of the listed elements it would be hardest to remove an electron from Flourine as the positive nucleus close to the electron orbitals has greater attractive force.

Helium has the smallest atomic radius. This is due to trends in the periodic table, and the effective nuclear charge that holds the valence electrons close to the nucleus. Atomic radius decreases as you move across a period from left to right and decreases as you move up a group from bottom to top. Since He is at the upper right-hand corner of the table, it must have the smallest atomic radius.

The periodic table allows you to follow general guidelines or "trends" that are displayed on the table. Atomic radius is one such trend. As you move down in groups, further shells are added to the atom which results in an increase in radius. As you move to the right on the periodic table, the nuclear charge increases which pulls the elctrons closer to the nucleus. As a result, the atomic radius will decrease when moving to the right.

Atomic radius decreases as you move left to right on the periodic table. As atomic number increases, so does the number of positive protons in the nucleus. To the far left of a period, electrons are widespread within a new electronic shell. To the far right of the period, the electrons still occupy the same shell, but experience greater attractive force toward the nucleus due to the higher number of protons present.

While it is true that flourine is the most electronegative element, this does not influence atomic radius (though the two trends follow similar patterns).

The atomic radius of elements decreases as one moves from left to right across the periodic table. The degree to which lithium has a larger atomic radius than fluorine is most similar to the difference between another pair of elements within the same groups, that are also found on the left and right sides of the table.

Fluorine and chlorine are both halogens, and lithium and sodium are both alkali metals. Fluorine and lithium are both in the second period, and sodium and chlorine are both in the third. As you move from lithium to fluorine across the table, you will see similar changes and patterns as if you were moving from sodium to chlorine.

When predicting how atomic radius will change as you move along the periodic table, remember these two trends.

1. As you move down the table in a given group, the atomic radius of the atoms will increase.

2. As you move left to right in a given period, the atomic radius will decrease.

Knowing this, we can compare the possible options. Sulfur and chlorine are in the lowest period, so they have the largest atomic radii. Because sulfur is to the left of chlorine on the periodic table, it will have a larger atomic radius. As a result, sulfur has the largest atomic radius out of the possible options.