New gal from UT here! Need some help.
1/2aFish, excellent rundown of things to check!
I hope you don't mind if I use your recommendations as an outline for making a few suggestions of my own.
First, get a Factory Service Manual for it.
I would add that if you keep an eye open, you may be able to get an original printed copy on eBay for a reasonable price. You have to be patient, and it won't be perfect (greasy fingerprints on the pages, etc.), but sometimes, such as with illustrations or wiring diagrams, there's no substitute for an original manual.
Also, if it's available for your year, download a Parts Manual from MyMoPars too.
Sometimes they're invaluable for finding some tiny fact, with certainty, rather than by internet rumor, and the original factory part numbers can make searching for parts much easier.
Tires - Old tires used just to putt around town at low speeds while sorting out what you have is less of a concern...
Agreed. Don't sweat it for a bit of low-speed rolling, but make sure they're good if you're going to do any real driving.
In addition, just buy a set of spring kits and adjuster kits, and a pair of front wheel bearing seals now. They're dirt cheap, and you'll be happier if you have them on hand when you pull the drums, if you find something is AFU (which is not unusual – these things can be pretty far gone and still seem to work fine).
Also, check your rear emergency brake cables – make sure they actually slide.
If they're stuck, buy a pair of them, too.
Steering - If you sit in it with the engine off, does the wheel turn a lot before you meet resistance from the tires starting to turn?
I would add that (if this is a p/s car) the stock power steering box is a bit loose compared to modern standards, even when not worn at all, so don't be surprised. If a bit worn, it can often be tightened up by tightening the big adjuster screw on top (which is outside the purview of this thread).
Importantly,
unlike the GM (Saginaw) steering boxes, the Chrysler steering box gets tighter with the engine running. They will all be sloppy with the engine off.
Jack up the car (use jackstands), start the engine, crawl underneath, and have a friend wiggle the steering wheel back and forth over and over again. Look at, and feel, all of the ball joints, the steering column coupler, etc. There should be no play. If there is, that part needs replacement. Sometimes, wrapping your hand around an entire ball joint assembly will let you feel relative motion that you can't see.
Electrical - This has been addressed, but yes it's a good idea to sort this out promptly. In addition to your wonky flickering issue I'd go through and turn on everything to make sure all items are working properly.
Flickering and erratic ammeter sounds like a loose connection. Stare at, meditate on, and understand the factory schematic, then check every feed wire.
Have a friend systematically wiggle every wire and connection as you sit in the car with the engine running and the affected accessories on, and watch the ammeter, and see if you can localize it. You'll either find it or you won't, but this is fairly easy and doesn't cost anything.
Belts and hoses - Unless they are clearly new I replace all of these and save the old ones for spares in the trunk should I need one while out and about.
This. Exactly. And old radiator hoses will feel "spongy," and will bulge at the ends where they're clamped on.
Tune-up - Do a basic tune-up and replace the cap, rotor, points, condenser, and plugs. If the wires are old, stiff, or cracked replace them too.
@halifaxhops is a quality member here who sells the good stuff (not Chinese junk) for a tune-up.
Yes. No Chinese ignition parts. Good, old-stock American parts are still around, and are sometimes even cheaper. Standard Blue Streak parts were made substantially better, but that changed somewhere around 20 years ago. You can still find original stock from before this if you look. And check with Halifax, as Fish says.
I saw you just filled your gas tank, get some Sta-Bil from the parts store and treat the gas. That will help it last quite a while.
Depending on where you live, if non-ethanol gasoline is available it will last longer, and your car will probably run better, as the carburetor is set up to provide a set air-fuel ratio, which was optimized for non-ethanol fuel. It's more expensive, but is often worth it.
Most of this car-fixing thing is experience and feel, as well as logical thinking.
Practice will get you better at all three, and having someone experienced (not a ding-dong or a numb-nut) to show you something every now and then can be invaluable.
Good luck! You'll do fine!
– Eric