Well as you go down the periodic table, the size of the atoms will increase because of the addition of higher energy levels, increasing atomic radius. However, when you go across the periodic table to the right, the electrostatic force between electrons causes them to become more compact and smaller. However, once the energy level is completely filled with electrons, the atom (noble gas) is larger.
I agree with everything except the last sentence. There is no reason for the noble gas atoms to break out of the general scheme. They are the smallest atoms within a period. However, between a noble gas atom of one period and the alkali metal of the next period, the radius rises sharply, because the next period starts a new electron shell.
I imagine that the helium ion would be smaller... because it has less protons than lithium does... but there is also the fact that since there are less protons than lithium, there is less electrostatic attraction, and so the electrons are not held in as close for the helium ion. I feel that this more likely explains why a helium ion is not likely to stay as an ion for very long. Am I correct?
Okay, thank you for helping me clear that up! So He- is larger than Ne because although they are on the same energy level, He- has less of an electrostatic attraction, being that it has less protons, and so the electrons are not bound as tightly to the nucleus as they would be with Ne.