I've got a nice vintage road bike, and I want to upgrade the brake levers, and probably the handlebars as well.

Right now it has older levers that seem to jut out from the middle of the handlebar curve, kinda like this pic


I also have another bike that has bullhorns, and I love how the tops of the bars have all that flat real estate for my hands.

Its my understanding that with modern brake levers and a modern shaped handlebar, it'll be more like bullhorns when I'm riding on the brake hoods.
Right?

Maybe shaped more like this?



Can anyone recommend some good brakes?
I don't need it to have integrated shifters, I've got down tube shifters.
Also, nothing with the brake cable shooting out the top like my old ones.
I assume my old calipers will still work with any modern lever, right?

Thanks for any advice!