Lots of options, and most road bike brakes will work ok. If you don’t like the shimano copies - there are campy copies, old-style single pivots, fancy “aero” and if you don’t need to slow much with the brake- cool looking modolos
I run BMX levers near the stem on my two fixeds. I have to pry them open further to fit them on the track drops, but they work fine. I ride mainly on the top. I’ve used the same lever on flop n’ chopped bullhorns too. They were like $9 for the levers, they’re “Pro Rush” or something.
have a look around for a lever designed to work with road calipers, or cantilever brakes.
if you use aa MTB lever, you’ll get very weak, wooden brake performance.
cross levers are pretty good, and if you don’t mind the large size, shimano road set deore levers are great. good feel, and lots of power to the caliper.