Personally, I never let my fingers touch a solution when printing. That ensures my fingers stay dry and chemical free, so I don't inadvertently contaminate my fresh paper stock.
The paper is slid into the developer tray and I have a set of tongs in each tray that stay in that tray. The print is moved from one solution to the next by tongs, but only in one direction. For example, the developer tongs will be used to move the print to the stop bath, the stop bath tongs to move to the fixer and the fixer tongs to the wash. I'd never use fixer tongs to remove a print from the stop. However, I am careful that when the print is moved into the next solution the tongs don't touch the next solution.
From the stop to fix for example, I lift the print out of the stop, let it drain vertically against the side of the tray. Then I move the print over the fixer tray and let it go. Then I switch to the fix tongs and move the print into the tray and adjust.
This ensures that I always have solutions moving in the same direction as the print, and there isn't any backwards contamination, such as fix into the stop. I'm very methodical to ensure there is no "upstream" contamination if you like and I'm also very rigorous about separating dry side and wet sides of the darkroom. I want to keep the enlarger and unexposed paper away from the wet side.