You have turned an important corner. Once you get used to wearing one, you will never go back. I have worn a bra every day for the past 3 1/2 years and seldom leave the house without one. With a few minor adjustments in the type of shirts you wear, you will become so confident you don't even worry about anybody noticing it. That first trip to Home Depot is scary but you can do it.
I wear mostly pullover type leisure bras because they don't have hooks or strap adjusters to show through my shirt, but I have been test driving some underwires lately. When I took off my bra last night, I realized I had been wearing it for 16 hours straight and could have gone a few more comfortably. Now that you have made that first step, I encourage you to try different styles and fine tune the sizing until you find the ones that suit you. Ask questions, that is what we are here for.