Unlike most of the folks on here, I find a pullover type leisure or low impact sports bra to be perfectly adequate for daily wear and even for activities like mountain biking. I have accepted and enjoy my breasts and don't mind that they are somewhat obvious but I am still a bit bashful about wearing a bra that shows through my shirt. The pullovers don't have any hardware on the back and they lie flat under your clothes. I have been wearing Rhonda Shear Ahh bras almost exclusively for 4 or 5 years. I wear one nearly every day and having somebody notice my bra is the farthest thing from my mind.
https://rhondashear.com/products/the-original-ahh-bra?variant=15404481020006Recently I picked up one of these in a thrift store and immediately ordered 2 more of them. This is my new favorite bra. For what it's worth, I wear an XL in the Rhonda Shear but need a 2XL in the Hanes for the same fit. I wear a 42C underwire. These aren't for everybody but they work for me. If you are much bigger than a C cup, you probably need a big girl bra. If you are coming to terms with the fact that you may need a bra, these are a great place to start. Cup sizing is not an issue and they are inexpensive. Nobody will know you are wearing it.
https://www.hanes.com/hanes-get-cozy-pullover-comfortflex-fit-wirefree-bra.htmlI also like the looks of this one and plan to order one in the near future.
https://www.hanes.com/dhhu39.htmlI have a Fruit of the Loom underwire I like a lot but don't wear it often because the strap adjusters are so big they show under a fleece vest. I mostly wear it for carpentry and yard work when I don't care who sees it.
My wife has a couple of these I borrow once in a while. We are fortunate that we can wear each other's bras and she is OK with it.
https://www.balibras.com/lace-desire-reg-underwire-bra.htmlAs somebody has noted elsewhere, most people either don't notice my boobs or they just don't care. When I do catch somebody whispering and sneaking furtive looks at my chest, it is always women. People with breasts notice other people's breasts. I find myself looking at women to see if I can tell what type of bra they are wearing, including TV actresses. I think on the whole, both men and women are tending to have larger breasts than they used to, probably due to prescription medications that are ending up in the water supply. Try watching some old Columbo or McMillan and Wife episodes and see how many of the women have large breasts. Now take a walk through Walmart and do the same thing. I usually spot a few men with gyno, usually because their breasts look like 2 puppies in a towsack. A bra of any kind will make them a lot less obvious. Try it, you won't go back.