If you just want to see the engine run, the only wiring you need is from the battery to the coil and from the coil to the distributor. The coil feed can be taken from the starter solenoid. However, if you are using a 12V battery, you should connect a resistor in series with the coil to avoid burning the points. Don't make the final connection at the coil or battery until you are actually ready to start the engine (same reason - you don't want to burn the points). If the carb switch and relay aren't connected or operational, you can jump the solenoid with a screwdriver to crank the engine, but don't try this just yet.
That takes care of the wiring, but if you are attempting to start an engine which has been sitting for a long while, you need to do a few other things first. If you can get any history on the car specifically relating to why it was put into storage, please tell us about it before going any farther. In other words, you want to know what problems the engine had the last time it ran (or wouldn't run) before you attempt to start it.
If you don't hear about anything bad, take off the valve cover and turn the engine two full revolutions by hand. This is mainly to check for stuck valves so you don't bend any pushrods. Of course if you can't turn the engine at all, you have more serious problems and shouldn't attempt to use the starter until you can get the engine free.
If the engine turns freely, loosen the oil drain plug just enough to see what runs out. If you get water or anything else other than reasonably clean oil, drain it all and replace with new oil.
You won't need to worry about the cooling system for the first starting try. If you want to run the engine for longer than a minute or two, then fill up the radiator and check for leaks.
Don't attempt to start the engine on the gasoline that is in the tank. Disconnect the inlet line from the fuel pump and temporarily run a hose from the pump to a can with fresh gas in it. Disconnect the fuel line at the carb end and crank the engine a few revolutions to make sure you are getting gas to the carb. Then reconnect the fuel line.
Next, check for spark. You may need a helper for this. Connect battery power to the coil and pull the wire out of the distributor cap center terminal. Hold the end of the wire about 1/4" away from any metal part of the engine and crank the engine or have your helper crank it. If no spark, you will need to troubleshoot the ignition system before going any further.
Once you know you have spark, remove the air filter and open the choke so you can look down inside the carb. Operate the throttle lever and see if you are getting a squirt from the accelerator pump. The float bowl should be pretty much full from the spark test, so if no squirt, the accelerator pump probably needs attention, but you don't need to worry about this right now. Instead, just pour about a tablespoon of gas down the carb for an initial prime.
Connect power to the ignition and crank the engine. It should fire almost immediately on the prime, but if it won't keep running you may have other problems inside the carb that will need attending to.
As soon as the engine starts, check the oil pressure gauge before you do anything else. If no pressure, shut it down immediately. Otherwise, keep the engine running and check for fuel leaks at the carb to avoid any fire hazard.
If you need additional info, feel free to ask.