You may have a hard time mounting regular road brakes on the bars unless you use chopped drop bars. I have three bikes setup with bullhorn bars and all have bar end brake levers. Two have stem mounted shifters and the other has thumb shifters mounted on the tops.
Another option is to use cyclocross levers by themselves and bar end shifters.
I have read that no Shimano shifter will work with a SRAM derailleur because they need a 1:1 cable pull ratio and Shimano uses 2:1.