TBH the champion you play doesn't have a huge impact on how you 'play safe' as a playstyle, it just changes what safe means.
For someone like Janna, "safe" can sometimes mean seiging them under their turret if you have wards set up since you have so many peel tools that you'd still be safe even if a gank or roam appeared. Playing "safe" with something weird and janky like vayne support on the other hand would basically mean never leaving under your tower.
Most of the suggestions people have mentioned are good at peeling and making things safe for your adc if they're failing to be safe themselves, but since you mentioned it was you throwing when behind it sounds more like a playstyle issue for you rather than your adc. Remember, playing safe is a playstyle, not a champion pick. Pretty much every champion can be played safely and pretty much everyone can be played aggro as the situation warrants, it's just a matter of having the self-discipline to actually do so.