I’d start by looking at the ignition timing and check/replace the points and condenser. With the ignition timing skewed or the dwell way off, the engine will be hard to start, idle weird, and bog out. Also check the centrifugal advance mechanism under the distributor cap to make sure it isn’t sticking and the vacuum diaphragm that operates the vacuum advance and the vacuum line to it. I really suspect the bulk of your problems are ignition timing related.
db4690–haha–I feel old too, I haven’t used my timing light since about the mid 90’s when mechanics started using scanners to check timing. True that even though electronic ignition came out around 1976, you could still set timing on those distributors.
Yeah, I used my timing light to check the ignition timing on brother’s older Toyota.
I had cleaned the throttle body and IAC, and then I had to slightly tweak the idle speed
Afterwards, I wanted to make sure the timing was still good. It was right on the money
I have a snap on scanner, but the software for those older Japanese cars is terrible. It wasn’t even worth hooking it up.
I’m absolutely in agreement that this sounds like a carb problem. Be sure you get a kit with a new float. I’m betting you’ll need it. I’m betting the old one is no longer working very well. And any kit worth its salt will have new needle valve parts in it.
Mustangman can probably confirm what type of float this is. Some were made of materials that eventually broke down and became saturated. And the needle valves that they opened and closed to regulate the fuel in the bowl get gummed up over the years. Having rebuilt a few one barrels, these are the usual problems… along with rubber breakdown on seals and accelerator pumps.
The dwell/tach and vacuum gages are essential as well, and a cheap investment. Harbor Freight Tools sells them if you can’t find one locally, and their prices are good. I recommend an inductive pickup on the dwell/tach.
@UncleTurbo I will get some for sure. Thank you. I never would have known 
@"oldtimer 11" thank you. I’ll be writing that down as well
@"karl sieger" This really helps. I was wondering which was the best type to get.
@"EK Hammer" I changed them one at a time. I was letting the car run yesterday and it idled kind of high and never “settled down,” for lack of a better term. I took the clear hose off the vac and it settled right down. Is that normal?
@GeorgeSanJose thank you. It’s been an adventure so far, but fun (with a few choice words). I pretty much started driving the car right when I got it as a daily driver. I’ve just been fixing and buying the tools as I go. It looks like I’ll be buying quite a few of them for this one. I usually go poking around my Papa’s garage before I buy anything. This time I wasn’t so lucky.
I’ll keep you guys posted!
@stenotab
If I were you, I’d be looking for a used snap on timing light on ebay
Once you get the tools, make sure you have some instructions on how to use them on your Chevy. For example, you don’t just hook up the timing light, you have to disconnect and plug the vacuum advance and make sure the rpms are to spec. And before that, you have to adjust the points, because changing the point gap changes the timing.
Make sure that the heat riser valve is not stuck. It’s below the carburetor, in the exhaust manifold. If stuck, the engine may not run well. Mine always wanted to eventually stick; don’t know why, rust maybe? I owned a '63; had little trouble keeping it running right but by the time I got rid of it, it was only 5 years old so I can’t speak for old spark plug wires.