First visit the LC Smith Collector site. It is a great resource
http://www.lcsmith.org/ Now to the question of overall restoration.
Before you restore you must carefully evaluate the gun.
The gunsmith must check the barrels for minimum wall thickness (as a general rule I believe that a 20 gauge gun should have .025, if less than this you may want to spend your money elsewhere or stick to low pressure loads only)(low pressure is not a war stopper but less than .020 is)
http://www.parkerguns.org/pages/faq/BarrelThickness.htm The barrels must be checked to ensure the gun is on face (check this by removing the forend and see if there is any movement in the barrels on the receiver)
Is there sideways movement between the barrel and receiver with the gun open?
If an ejector gun the ejectors must be checked for timing (if they properly work)(check with either snap cap or already fired shells, see if they properly eject when one or the other chamber is fired and when both are fired and if they throw the spent hulls about the same distance and place)
The Hunter One Trigger (HOT) is a good trigger when working. It needs to be checked both dry firing (with snap caps or spent hulls) and with live shells. It needs to be checked with first right then left then left then right. It further must be checked with live ammo.
Check does the trigger pull feel correct for you
Check the operation of the safety (remember snap caps-spent shells)
Is the top lever right of center? Left of center suggests a worn rotating bolt. Does the top lever stay in the open position when the gun is open? Does it snap to the closed position forcefully?
The condition of the stock must be looked at carefully for cracks at the end of the locks (probably not likely on a quality restock but look at it carefully) With the locks off look at the angle of the wood around the locks
If the stock needs a refinish or recut of checkering go for it, but only if very worn. It is probably not worth trying to make an old gun too new, but that is ultimately a matter of taste.
Hold back on stock refinish and alterations until you have shot it some to determine if it fits you properly, if you need to change something it is beetter to do it all at once.
Consider getting an LC Smith Cocking tool
http://www.doublegunshop.com/forums/ubbthreads.php?ubb=showflat&Number=341751&#Post341751Lastly understand that one rarely breaks even, or makes money on a restoration even if your objective is not to sell.