I have been out of the business for a very long time. It is rare to see a question relating to older vehicles. I am a former class A repairman at new car dealers, I was certified in all 8 categories by NIASE in 1974, one of 4 % that passed all 8 tests. Because of the low number of passing grades, they made the test much simpler, now anyone that can lift a wrench is "certified technician." You don't see the old "General Automotive Repairman" patches with the 8 (or however many tests you passed), under it, they were blu and yellow. But I digress by bragging.
The best method to adjust a carb i to use a tachometer or the very common, (back then), tach and dwell meter, they are inexpensive and vital with the year of your car. Engine warm, hook up meter, this is very, vsry simple with the clip on wires attached to the meter. Use a screwdriver to turn the mixture screw until the highest reading is obtained, carb is now adjusted.
The other use for the meter is the Dwell Angle reading, this allows you to insure the ignition point gap is correctly set on you engine. This adjustment should be done before the carb adjustment. The meter is connected the same way. The dwell angle is determined by the number of cylinders in your engine; an 8 cyl. engine requires a 30 degree reading, a 6 cyl. engine requires a 45 degree reading on the meter. This adjustment is tricky to the novice. It is accomplished by setting the air gap between the contacts on the ignition points under the distributor cap, you need the specs for your engine on the air gap. The only break is on 8 cyl. GM made cars, they have a lttle door on the distributor cap that you can use to access the point adjustment setting with an allen wrench. For this type of set up, slide the allen wrench in, start the engine, adjust to 30 degrees. On all other engines you need to set the gap to the spec with a feeler gauge of the proper size, then put distributor cap back on and start engine to confirm proper dwell angle on the meter. If you are handy, I am going to give you a short cut that works perfectly; remove distributor cap, replace points if they are pitted or worn, you must change the condenser also, you must, it is a small silver cylinder shaped object that is wired to the points. Install the new points and condenser if needed. With the distributor cap off slightly loosen the 1 screw that hold the points in place, and, I mean slightly, you should have some resistance if you try to move the points adjustment gap, have someone crank the engine while you adjust the air gap until the dwell meter tells reads the angle you are trying to set. This, to me is the best method, it kind of lets you adjust any car like the 8 cyl GM products with that little door. Don't forget to check the distributor cap, remove it and look inside for pitting or wear on the contacts, check the rotor for wear, you may want to check the ignition wires as well since you mention backfiring. If you have an OHM meter, you can connect one of the two probes to the end of the ignition wire where it hooks up to the spark plug, the other probe should touch the inside of the distributor cap contact for the same wire, check for a reading on the meter, if no reading is found the cylinder that wire connects to is not getting the spark it requires. If the backfiring is happening all the time, check the firing order as well, that is found on the intake manifold mos of the tme. Good luck.