Get the drivetrain up to par, a quality transmission, I like a nice built 4l60e there's no reason it can't be somewhat streetable. Next up is a rearend and driveshaft, 12 bolt or 9", I'd suggest the 9" with a spool. Pick up a quality driveshaft, precision shaft is great with the 1350 u-joints. Quality set of shocks and springs, QA1s or Afcos, and a Madman torque arm. Get a nice set of drag wheels and tires with a good 10.5" radial.
Now for the fun part, there's 2 ways I'd go to make power both will cost about the same give or take. Start with building a fuel system, make it a return system, do a pair of 255 Walbros, and then decide on either nitrous or turbo. If nitrous buy a high end set of heads and an aggressive camshaft suitable for spray, supporting mods for head and cam swap, and then buy a complete nitrous set-up and since bracket racing is the goal a nitrogen assist system to regulate the nitrous system for super consistancy. If turbo, buy the biggest set of injectors, a nice hot side set up, quality 76mm turbo, and all other turbo parts. Get a ported set of 6.0L heads and a good turbo grind cam, and LS6 intake.
This could obviously be done a few different ways, but I'd like to drive it on the street and going to a turbo 350 or 400 you'd loose the lock-up converter and overdrive. A spool isn't bad if you don't try to go parrallel parking.
Over all just throw $15k+ at it, and it'll run low 10s all day every day.