When looking at bras try to get ones that don’t have the strap adjusters on the back because they will show and don’t get one too tight because it could show side fat lines at your back. I underdress daily and have found some sports bras without cups are very stealthy and still give you that feeling of a bra hugging you all day. If the bra or bralette is a racer back make sure the straps don’t show at your neckline. As far as straps go, get thin or flat straps without padding on the shoulders. It makes no difference if the bra is underwired or not if you wear a loose top but look for extra cup material bunching on your chest making visible lines. If you wear a cami or short slip it will help hide bra lines.
I never worry about panty lines showing but you may look for those if wearing tight bottoms. If you wear pantyhose or garters and hose be aware of a swishing noise when you walk with some pants and if no socks then the nylons will show at your ankles.
Experiment with different items and check yourself out front and back in a mirror before going outside. I once found my bra outline was visible to everyone after being out but I couldn’t see it at home until I got in the right lighting.
Good luck and have fun… underdressing is so thrilling when you have a little secret among the vanillas.