Hi Releca,
I would second what Grace said, both about the visibility & about the effects of binding.
I have been wearing size "S-junior" nylon/spandex tank tops under my work shirt for months without anyone noticing the C-cups on my 5'11" 170lb frame. I have been told by a couple of colleagues (who know I am trans) that anything that might be noticeable is assumed to be the normal "manboobs" common to most 40-something-year-old men. Both of them only see me as male even though they know I am trans and have met me outside of work. That said, Philadelphia does seem to be a bit more trans-friendly than most places.
I did try to wear a compression vest once. I didn't last more than 2 minutes before my dysphoria spiked so much that I almost ripped it off.
Sports bras are still bras. They do a good job of containing what is there so that it does not move much, but do maintain something of a feminine shape while doing so. This observation was brought to my attention by a couple of transmen who were less than enthused about sports bra's effectiveness.
Hope this helps.
Be well,
Tessa
Edited for spelling.