I'm not sure if I'm right, but this is how I would approach it:
First set (Cl, S2-, K, K+, O). Check if this is an isoelectric series: not all of them are. Shell will usually determine size to the greatest extent (e.g. 2nd shell will always be a lot bigger than the 1st shell) and anions/cations are always a lot bigger/smaller than the neutral species, respectively. In this set O is in the 2nd shell, so it will be the smallest. K is in the 4th shell, so it will be largest. The remaining (Cl, S 2-, K+) are all in the third shell in terms of electrons. K+ and S 2- have an equal number of electrons but we know that K+ has a larger/stronger nucleus, so it must be smaller than S 2- (pulls an equal amount of electrons in tighter). So far that makes the ranking in size from largest to smallest: K > S 2- > K+ > O. Cl doesn't have an equal number of electrons to the rest in its row, so I have no idea how to place it: it's likely smaller than S 2- because it has a stronger nucleus and less electrons, but I'm not sure if it can be easily distinguished from K+ in terms of size. This leaves me with: K > S 2- > ?Cl, K+? > O
Second set (S 2-, F-, Ne, K+, and Ca 2+). Check if this is an isoelectric series: not all of them are. Based on # of electrons, F- and Ne will be in the 2nd shell (smaller) and the other three will be in the 3rd shell (larger). This one is a bit easier because the ones in the same shell/row are isoelectric: F- and Ne have the same # of electrons but Ne has the larger/stronger nucleus, pulls its electrons in tighter, so F- > Ne in size. S 2-, K+, and Ca 2+ are also isoelectric, so once again we use the strength of the nucleus to distinguish size: Ca 2+ has the largest/strongest nucleus (so it will be the smallest ion), then K+ will be larger, then S 2- largest. This makes our final ranking here from largest to smallest: S 2- > K+ > Ca 2+ > F- > Ne.
I distinguish them on the basis of shell (in terms of # of electrons), and then if they are within the same shell, I hope it's an isoelectric series and figure it out that way.