For balancing, the shop's going to need everything from the balancer to the flywheel/flexplate. Bring them the crank, pistons, rods, pins, rings, bearings, everything. All of this stuff will affect the bobweight and will need to be present to properly balance the rotating assembly. Most shops won't let you into the work area due to insurance regulations, so you probably won't be able to watch. Here's a rundown of the balancing process.
Your pistons and rods should all be within a gram of each other. The big end and small end of the rods must be weighed seperately and equalled in weight matching big end to big end and small end to small end. Once we're all equalled out, we need to calculate the bobweight. Calculating bob weights isn't too difficult, but it is necessary to properly balance the engine. Here's a list for determining bobweights for balancing. This is based on an internally ballanced engine. Things change a little bit when you're going external as the flywheel/flexplate and balancer come into play.
Rotating Weight:
Big end of rod (including fastening hardware)
Bearing
Oil (normally estimated at four grams)
Reciprocating Weight:
Piston
Wristpin
Pin locks (if used)
Small end of rod
Piston rings
Bob weight = Rotating Weight + Reciprocating Weight x .50
Once everything is equal and the bobweight is determined, weight is added to the rod journals equalling the bobweight that was calculated earlier. A balance machine is used to specify exactly where the crank needs to be re-worked to bring it into balance. This is done by adding or removing weight from the crank in specific places as determined by the balance machine. To remove weight, the shop will generally drill holes in the counterweight. To add weight gets real expensive real fast. Most crank manufacturers can supply you with a "target bobweight" for their cranks helping you try to pick properly weighted parts to avoid the expense of adding weight to the crank. Shops will add weight in one of two ways. One is to drill a hole in the bottom of the counterweight and press in a slug of "mallory metal" (a tungsten alloy 1.5x heavier than lead and real expensive) and weld it in place so the reciprocating force can't throw it out. The second is to drill a hole parallel to the crank centerline in the counterweight and press in a slug of mallory. The position of the slug keeping it in place. In external balancing, weight is added and removed from the balancer and flywheel/flexplate instead of the crank.
I hope this helps you to understand how things work and will help you in picking the proper parts for your build. As far as reputable shops, there are quite a few in the tri-state are, just do your research carefully. Good luck!