While strictly speaking nobody needs to wear a bra, in your case a bra would bring great benefit in comfort, support and stability to your breasts and I support your decision to wear one. My breasts are smaller but I also wear a bra virtually every day as the benefits outweigh any other considerations.
You are right. And I remember that you also like the Triumph Doreen bras just as I do. But although I'm now in some of my other bras a full 40D, the Doreen of 40C is even a little too large in the upper cup. But it's not that much that it is visible through shirts. Thus it's always good to get a fitting.