Not to contradict Rick and Enter the Flagon completely, but you may not have to shell out as much as they estimate, depending upon the condition of the car. The first thing you should do is pick up a copy of Hemmings Motor News. That’ll give you a source and prices on parts for the beast. Also check out some of the various hotrod magazines as they’ll have ads for aftermarket items (such as digital dashes, etc.) that may not be listed in Hemmings.
Now to beat some of the costs. Look for swap meets in your area, those can often provide bargains for things that you’re looking for (I picked up a mint condition factory service manual for my Chrysler for $20 and most places want more than that for a reprint.) Were I you, I’d just junk the A/C unit and go for an aftermarket model (Vintage Air seems to be popular with the hotrod set). The ones I’ve seen prices for are cheaper than the prices you’ve been quoted in this thread for rebuilding yours, which would have to be converted to handle new coolant anyway. You might be able to do the interior yourself, as lots of companies make kits for classic cars (this is where Hemmings comes in handy) and if you can find one for your car, then it’s reasonably easy to install.
Hemmings will also have listings of scrapyards that will have parts for your car (and IIRC, Lincoln’s had the same basic body style for a number of years, so you shouldn’t have trouble getting parts you might need), and those will often be cheaper than reproduction parts.
I would not recommend spending less than a couple of grand for a new paint job, unless the painter is a friend of yours. Generally, $300 paint jobs look like they were applied with a brush.
One way that you might be able to get a modern dash (and Rick would be able to tell you if this was possible or not) would be to find a wrecked vehicle with the same size wheelbase as your Lincoln and unbolt the body of the wrecked vehicle and bolt your Lincoln’s body to that. That way you wouldn’t have to deal with all the conversion crap.
As for uprgrading the suspension, that’s not too terribly difficult, depending upon the original suspension that the car was equipped with. If it has the air ride suspension, then forget it. Those things are the biggest PITA known to man. Generally, you can pick up new tie rods, ball joints, etc. fairly inexpensively, and with the right tools, you can do the job yourself (save the alignment) in an afternoon.
The one thing that you absolutely must check on, is if the car has a dual or single brake master cylinder. If it has a single, then before you do ANYTHING to the car, swap it out with a dual cylinder! I owned a car with a single master cylinder and had a wheel cylinder rupture on me, which meant I had no brakes. Damn near got killed before I was able to stop the car (using the “Fred Flintstone method” I might add). It is not an experience I care to repeat.
Another thing you’re going to want to find is a shop in your area where the guys have experience working on carbs. Unless you drop a modern engine in the car, that is. Many of the young guys out there haven’t worked on a carb, so they’ll be lost if the thing needs adjusting (or rebuilt). The Car Talk website used to have listings (and might still) of listener recommended shops. I’d check there to get an idea of the shops in your area, so if you run into something that you can’t fix, you’ll be able to take it someplace where they can do the job right.
Pick up a book on restoring old cars, and pay close attention to the kinds of tools you’ll need as well as how to use them. Unless you get a modern engine (or modern ignition system) you’re going to need a dwell meter and timing light. Buy yourself two complete sets of tools, as well. One set (the good one), keep at home, the other (a cheap one), keep in the car, along with the factory service manual, so that you can make emergency repairs on the road if you have to.
Also, find a car club for your Lincoln and join that. At least some of the guys in the club will work on their own cars and will have figured out solutions to the various quirks that your car has. This comes in handy if the original parts are hard to find, or there’s a problem with the design of some aspect of the car. (They’ll also know good places to take your car, where to get parts inexpensively, and may have spares they’d be willing to sell or trade.)
Finally, once you get the car restored, keep buying parts for it! That way when something goes wrong, you’ll have a replacement part handy and won’t have to try to find one.
Lastly, if body mount bushings aren’t available, you can improvise one by drilling a hole in a hockey puck and using that.