I have been wearing bras for nearly 6 years now and never leave the house without one. After some trial and error, I arrived at the conclusion that a leisure bra was quite adequate for my needs. They don't lift and shape the underarm boob like an underwire does, but they do keep things from moving around. I even wear one for mountain biking, which is why I ended up needing a bra in the first place.
My first choice has been the Rhonda Shear Ahhh Bra. They are inexpensive and there are no hooks or strap adjusters to show through my clothes. I have caught people staring at my chest (always women), but I think they are seeing the breasts, not the bra, so I never give that a second thought. They are sized according to chest measurement and the cups are one size fits all. As noted, they do compress the breasts a bit but not the way a sports bra does. Recently I have been switching over to the Hanes Get Cozy bra which is also a pullover but a bit more heavy duty.
If you are much bigger than a C cup, you should probably go get fitted for a big girl bra but I think a leisure bra is the perfect solution for a guy who wants to ease into bra wearing without the embarassment of getting fitted, at least until you are comfortable wearing one in public. The first trip to Home Depot is scary but you can do it.
That said, I do own several underwire bras which I wear occasionally. Recently I have gone several weeks at a time wearing nothing but underwires and I am comfortable with them, but I still find the pullovers adequate for most daily wear. YMMV. I know 90% of the guys on here prefer underwires, but there is a handful of us who love our pullovers.