Good question, Nel, and as you can see it generated a good amount of diverse answers!
Like others have said, yes, you can trust starsan at the right dilution as a no-rinse sanitizer. Make it too strong and you may get off flavors (although I don't know how strong that would have to be), and, as stated above, let the pH get higher than 3 and it loses its effectiveness. "Don't fear the foam"
We all have our bottle management routines, so take the best of what you hear that makes sense to you. Here's mine:
When I get a batch of bottles with labels, or get some returned to me in a gnarly state, I do a several-hour hot water rinse in sodium percarbonate, which removes just about everything except plastic labels, screen printing and petrol-based glues. Then, using a jet washer
I thoroughly rinse and inspect the bottle, sometimes hitting it with a bottle brush and/or scrubbie to remove anything left. Then they go into my dishwasher rack to dry. After that, I store them neck down in their crates.
With bottles that I've just emptied, I rinse thoroughly with hot water, let dry, and then store neck down in their crates. If I have any doubts about the empties, I'll clean them out with a bottle brush, rinse with the jet washer, dry and store.
On bottling day, I fill up my Vinator's reservoir
with star san, and get a two-handed rhythm going: two to three pumps on the vinator, dip the neck in the reservoir, set on the sanitized bottle tree
until I'm ready to fill. After all are sanitized, I toss the caps in the vinator reservoir, fill each bottle using a bottling bucket with the wand attached to the spigot with 2 inches of tubing, again making it a two handed operation, filling, grabbing the next bottle, resting the crown on the bottle, setting aside and moving on. Once all are filled, I crimp the crowns on all the bottles. I can get 21 liters bottled, including cleanup, in 90 minutes. I usually dump the starsan in the reservoir, because by then it looks pretty gnarly.
To mix up the star san, I make 5 US gallons at a time, and from that bucket I fill another 2-gallon bucket I use for any soaking, and top off my spray bottles. I usually go through it all before its pH goes up, but sometimes I dump it if I forget to put the lid on either bucker and it gets bugs - flies seem to love to die in it.