A 383 is a 350 block bored 0.030" over for a 4.030 diam. bore, with a crank using the 3.75" stroke from a 400 cu. in. The combination requires custom pistons to accommodate the longer 3.75" stroke to keep the pistons from popping out of the top of the block. There is an alternative to the 5.7" rod and pistons made for a 383, but we'll discuss the more common approach first. The custom pistons move the piston pin up in the piston to make the right height from the small end of the rod to the top of the piston. When I say custom pistons, I really mean "after-market" pistons as the 383 piston is so common that it is a shelf stock item, just not a GM produced part. This is such a common combination that all of the after-market piston makers and mail order parts houses are stocking the 383 piston in many configurations. Here is a link to JE Pistons / SRP and you can look up most any configuration you might want. http://www.srp.com/ (Look under "pro series" and log in as a guest)
One drawback to the piston configuration is the ring placement. With the pin moved up, there is less room for rings so they have to squish the 3 ring lands into a smaller area, this leaves the piston a little unstable and under high loads or in a loose bore, they will rock a little allowing compression to squeeze by and oil to migrate into the combustion chamber. You should have the pistons in hand when you take the block to the machine shop so they can match the bore to each piston. Use a very reputable machine shop with a power hone and torque plates to get the best fit recommended by the piston manufacturer.
Here's the first rule of mechanical relationships, and it applies to the 383 more than any other: "opposing components attempting to occupy the same space at the same time,, usually wind up occupying adjoining space at the bottom of the oil pan"
The easiest way to build a 383 is to use a stock rod length (5.7") This will require the least modifications to the block. The 3.75" stroke of the crank just doesn't fit into the 350 block. You will have to grind on the bottom of the bores and the pan rails to clear the larger counterweights and stroke. Make sure you have AT LEAST 0.030" clearance between the reciprocating assembly and the block. As I said, this has become such a common thing that most good machine shops know what and where and how much to remove. Rods are available that have had the rod bolt relocated or ground on to provide the necessary clearance. Some rods do not address the clearance problem so be careful with that selection. I have heard of guys who clearanced the block and completely assembled the bottom end, then when they stuck a very high lift cam in the block, the rod bolts hit the cam lobes. Needles to say, everything had to come out and taken apart for grinding on the rods. Some after-market rods use 12 point cap screws instead of bolts and nuts and are very well suited to the long stroke small block. There is an option to this, you could use a small lift or small base circle cam and high ratio rockers to achieve the desired valve lift.
The last item of major concern is the crankshaft. The common 383 crank is a 400 crank with the journals ground down to the size of the 350 mains. The problem with this is the weak cast 400 crank. The 383 is a real torque monster and the cast crank will work,,,but,,, you are putting a lot of money into this thing, do you really want to have it depend on a weak crank. Many quality forged after-market crankshafts are available which are tailored to the 383 application. Although they represent a considerable investment, they also should be considered cheap engine life insurance.
The 383 can be internally balanced (like your 350) or external balance as the 400 crank was intended. KNOW which your assembly was intended for and match the harmonic balancer and flywheel / flex plate to the balance. Internal balancing the 383 represents a considerable expense if you are using a cast crankshaft. The amount of work necessary may exceed $200 or $300. There comes a point of diminishing returns where a forged crank intended for internal balancing is more cost effective.