For sports bras, try making sure that the band is as level as possible when you first put it on, and give more care to the position of the back than the front. In my experience, leveling to the proper back position is more important than the front position. The front is likely to ride up if it was initially pulled down too far, or you had to really reach for something, and naturally tends to tuck under the inframammary fold, as it would for a woman.
From prior experience only, sports bras work best and move the least if you know exactly where the back should be, so it won't move much during the day and adjust the front to be level to that position. Being male, we aren't going to be able to "boomf out" enough to pull the elastic out from under our armpits completely, and that will take getting used to. If sports bras are the way forward, I suggest making sure they are both washed and worn at least twice before passing judgment. I've found that with sports bras the color/dye can actually make a very serious size difference (really ladies?), but after some legit use they seem to level out.
Sports bras are great; I don't know why so many men would prefer a pair of flabby, painful, "moobs" flopping about all day instead of corralling those things in a (generally) inconspicuous manner? Buy some button-downs and lose the T-Shirts; nobody will care/notice a thing.