It would involve a lot more than just an Arduino & some wiring obviously. And a lot of the car's charm is its low-tech originality.
Get yourself electronic ignition (Pertronix is a recommended brand) which replaces points and basically uses solid state electronics to fire the spark plugs, making them run much better and no more messing with points.
All engines need timing, but modern distributor-less motors do it automatically; timing should be a set it and forget it thing for the most part.
Then your carburetor is likely the issue for running rough, hard to start, etc. You could get a different more modern carburetor, but switching to fuel injection may be the way to go if you just want "turn the key and go". They make fuel injection systems that look and mount just like a carburetor but use more modern tech - look at FiTech, or Holley for solutions. Those are going to require you to add a sensor to the exhaust and a couple sensors around the motor (all included in the kit, but work to add), plus you'll probably need a new fuel pump that can put out much higher pressure (fuel injected cars use ~40-60psi fuel, carburetor is more like 3-5psi).
It stinks because it's burning raw fuel and you're not used to the smell of that thanks to today's cars with catalytic converters - they do sell them aftermarket that you could add in to your exhaust system as well.
At the end of the day, it's all very possible and there are open source projects like Megasquirt that could be a place to start, but going the open source route will be even MORE "fiddling around" than your current setup, so you may want to look at off-the-shelf EFI conversions. At least do yourself a favor and get Pertronix electronic ignition - it's a total game changer in terms of ease of starting, smoother running, and less hassle, and it doesn't cost much and is easy to do.
But for a digital solution, you're looking at an EFI conversion kit, with a ready made wiring harness to convert the necessary items to run the EFI. It is common enough to do that you'd have no trouble sourcing advice and if you like that kind of thing it would be a great project. I see Holley do good looking kits but I can't speak from experience sorry.
The difference between an ECU run V8 and an "analog" V8 is mostly in electronic control of ignition timing and fuel injection, and all the sensors needed for the ECU to know what's going on. I think just replacing the carb with an EFI carb kit would be a great project, but to take it further you would need to ditch the distributor and use coilpacks and ignitors controlled by the ECU, and a timing sensor to sense the position of the crank. At that point you need a full ECU and speeduino would do the trick, but there are supported manufactures of aftermarket ECUs as well like Haltech, Holley, Motec, and Link.