I agree with looking for a more complete example. The one you have could probably be brought back to life but the parts to do that would likely cost you more than it is worth.
Note that you will need a pair of carbs, not just one (motorcycles generally have one carb per cylinder). And unless you want to deal with re-jetting them you will also need an original airbox (bikespeak for what car people call an air cleaner).
You will also need all of the controls that belong on the handlebars (including the master cylinder and clutch lever assembly) and a lot more.
"Standard" was never an official Honda model name but is commonly used to refer to the original model that the later Custom and Deluxe versions were based on.
When these bikes were made the most common type of custom bike was the "chopper"; The term originated in the 1950s with people buying war surplus bikes and "chopping off" everything that wasn't needed (mostly the military accessories like rifle scabbards and the brackets that attached them to the frame). With the interstate highway system developing stability at speed became more important than precise steering at lower speeds (as needed on rock strewn &/or rutted dirt roads) so the original chopper guys increased the rake a bit to increase the trail and then added slightly longer forks to keep the front of the bike at the original height. By the '70s people that didn't really understand why the front end was altered and figured if some was good more must be better were building monstrosities that were barely rideable but people thought they looked cool. The factories decided they could sell more bikes if they produced "factory chopper" models that resembled what customizers were doing, with the forks kicked out a bit, "peanut" style tanks and stepped seats but without the bad handling. In Honda's case that meant a range of "Custom" models based on bikes already in their product line with model numbers ending in "C" such as the CX500C (if you check the steering head the VIN plate should indicate the model number as well as the Date of Manufacture and Model Year).
Welcome to the forum. Please add your location and your bike's model and model year to your profile so that you don't have to remember to tell us every time and we don't have to keep asking when you forget (see Forum Settings link in my signature).
And welcome to the world of antique vehicle ownership (they own us, not the other way around). Your bike is about 4 decades old and obviously hasn't had a lot of the maintenance necessary to keep it safe & reliable so it is highly recommended to download the Factory Shop Manual for your model (available through the CX Wiki - link in my signature) and go through all of the service procedures, regardless of whether your bike has reached the specified mileage. It will also help you figure out what is missing and how to install those parts.
I also recommend looking on all rubber parts with suspicion because rubber does not age gracefully. I'm pretty sure I see cracked tire sidewalls; If they are you don't need to check the date codes on them to know they are well over 5 years and due to be replaced old no matter how good they look & feel (old rubber simply cannot flow around the irregularities in the asphalt well enough to grip when leaned into a turn, especially if it is cool or wet).
I see the original rubber brake line hanging over the handlebars (do I see the caliper on the other end of it? Is it complete?). Manufacturers of rubber lines recommend replacing them every 2 or 3 fluid changes (= 5 or 6 years) so I recommend shopping for modern stainless braided ones (they last practically forever and double the life of the fluid).
And don't forget things like the rad hoses and the boot between the engine and swingarm (they can crack on the bottom where you don't see it).
