WARNING! Long post ahead. Top off your pint before you begin to be sure you will remain hydrated throughout.............
Hey BadSnookerPlayer, I think a lesson in Billiards Table Anatomy 101 is in order here. I have had several rants in the past to no apparent avail. Knowledge of the terminology of the table has been in a downward trend as the commentators continue to muddy the waters and dumb down the vernacular of our hobby for the viewing audiences. An intelligent player of the game should remain unaffected and should discuss matters using the correct descriptive jargon.
As it has been for 400 years, an English Billiards table (upon which the newfangled game of "Snooker" is played and came into popularity starting about 150 years ago) has definitive words used to describe sections of the table and relationships between them. To make definitions simple, stand with the table set for a frame of Snooker and prepare to breakoff placing White in the "D". You are standing at the bottom of the table. The Black ball is at the top of the table. Anything that is toward the Black spot side of anything else is "above" it; anything toward the Baulk end of the table is "below" it. Anything on the table surface that is to the left of the centerline at this moment will ALWAYS be on the left side of the table no matter where you may find yourself standing at some time in the future. So the "top left" pocket will ALWAYS be the top left pocket, even when you find yourself cueing off the Black cushion (that is to say the top left pocket is the corner pocket near the Black spot on the Green spot side of the table). In fact, with the popularity of Snooker, it has become vogue to use the phrase "Green side" or "Yellow side" in place of "left" or "right" in many cases. So with these simple rules, it is possible to describe all six pockets with clarity: Green pocket, middle left, top left, top right, middle right, and Yellow pocket (yes, you can certainly say "bottom left" or "bottom right" as well, but for purposes of Snooker, the colour names work well for these pockets).
So with that said, now we can speak uniformly of your scenario:
I agree with all that you stated but with a single exception. I believe the best opportunity for success will come using running side in either case, screw or follow. So now, with our new terminology, we can endeavour to describe this.
First, using follow, the easier scenario. If White came to rest exactly level with Blue (not above or below), then if you follow with White, it will end up in the middle left pocket right alongside the Blue you just potted. So let's move the White instead an inch or two above the Blue on its spot and about a foot or 18 inches away. This is very thick contact with Blue so using follow will result in White traveling round the houses (three cushions, around the bottom side of Green/Brown/Yellow, takes an awful lot of power). So let's go back and move White more like 3 or 4 inches above Blue at the same distance (and White is still on the "right" or "Yellow" side of the table). So now, if you stun the Blue into middle left, then White will travel directly toward Brown on spot. So you must follow or screw. If you screw, chances are that White will screw too much and will come back to the cushion side of Yellow (or perhaps strike the Yellow directly) instead of between Yellow and Brown as we desire. So in this case, better to strike slightly above center of the cue ball with power so the White will cross the stun line and pass between Green and Brown (on spots). Do you need any side? Depends on the angle....the thicker the contact with Blue, the less likely that side is required at all. The thinner the contact with Blue (but you have decided that follow is still the correct choice), then the more likely that you should use some running side (right hand side in this case). This concept is worth taking a pause to explain....
When White is struck to follow, it will ALWAYS initially travel along the stun line. If the stroke is perfectly full in the face, you will actually see the White come to a dead stop for just a moment (during which time it is actually "travelling along the stun line" but at a rate of 0 miles per hour) before it lurches forward as the top spin takes effect. So the point is this: the thicker the contact of White with object, the more the White will cross the stun line when the top spin takes hold. The thinner the contact, the less the White will cross the stun line. In other words, if White is well above the Blue on spot and you play a relatively thin contact to Blue with follow applied, the White really won't cross the stun line at all and White will likely contact Brown anyway, exactly the same as a plain, ol' stun shot. Follow requires some "thickness of contact" to work. So if faced with a "thickish" follow shot that you judge the White will travel between Green and Brown, you don't need side at all because White crossing stun line gives you significant angle to miss the Green outside on the rebound....easy to judge. BUT....if you have a "thinnish" contact and playing follow, the White won't cross the stun line much at all and it is very likely that it will strike Green on the rebound so it would be good to apply running side (right hand in this case) to assure getting outside the Green on rebound (that is, assuming that it did not hit Brown in the first place; if that is the case, you should have used screw instead).
Another short pause here.....very advanced play that we see by professionals can make all kinds of variations of this concept. For instance, maybe the pro does not want to travel outside the Green but wants to bring White back on the same path between the Green and Brown. How to do this? Reverse side along with the follow (the American, usefully descriptive term for this is "check side" and I have heard commentators use this term on occasion). Instead of the normal "angle of incidence equals angle of return", the check side will cause the White to travel right back on about the same line it came from, probably right out toward the Blue spot again between Green and Brown.
Now, let's move onto a similar scenario but choosing screw instead. As said earlier, if faced with a thickish contact, you would probably inadvertently screw too much pulling the White so far back from the stun line that you will end up drawing it to cushion side of Yellow or strike Yellow directly...not useful. (If you WANT to use screw for these thick shots, you can but the trick is to strike just a little bit below the equator of the White, NOT near the bottom of the ball like a normal screw shot), and you have to strike HARD to make the White travel far enough (thick contact takes so much pace out of the White ball....top spin or bottom spin put the pace back in; top spin much easier to put the pace back in unless you are Judd Trump or Jimmy White in his prime). So if faced with half ball or thinner, follow is a bad choice because you will probably hit Brown no matter. So instead play screw and you just need to draw White just slightly back away from the stun line to avoid Brown. Now think about the exact direction White is traveling after contact with Blue: toward Baulk cushion (moving down the table) but also it is traveling slightly from the left (Green side) to the right (Yellow side) to strike the Baulk cushion. So if you play your screw on center vertical line of the cue ball, very high probability White will contact Yellow on the rebound. If you play your screw with running (left hand) side, then the White will "kick" off the cushion to rebound to the outside of Yellow. If you play it with reverse side (right hand, "check" side if you will), then White will rebound back the same line it came, between Yellow and Brown, very similar to how we described the follow with check side. Very effective, very "professional", but much more difficult to control for a rank amateur such as myself.
So personally, I find it easier to play the running side to the outside of either Green or Yellow. Edit: Just to be absolutely clear (because I want to be sure I interpreted your post correctly), running side in these cases would be top right for follow and bottom left for screw. The degree of top right/bottom left (i.e., the EXACT position of cue tip on the White) is completely left to your judgement and will need to change as required for whatever variables may be involved in a particular shot.
If you are really disciplined, you should try to get all of these tools into your arsenal so the first step is to understand the physics behind why the balls move as they do so hopefully, this (admittedly lengthy) narrative may help you on this path.
Good luck Sunday!