I'll probably get a lot of flack here...
...but it's not always a good thing to go to bare metal. How many repaints has your Cougar been subjected to? If it's original or maybe 1 repaint, IMHO, you shouldn't go down to bare metal. 32 year old primer is about as good as it gets. If it's just caked on like my '70 was, (I counted 6 different colors,) than it's a better candidate. If that's the way you're gonna go and have any idea to do it yourself let me throw out a couple of ideas...
Although I haven't used it myself, I've noticed a water-soluable, non-toxic stripper being advertised. I believe you can get it from Eastwood. If you use it or regular stripper, I would only use it on large flat areas. Even though it neutralizes with water, if it gets into any cracks or seems it will come back to haunt you. When I stripped my convert, stem to stern, I used a combination of stripper for flat surfaces and a Scotch stripping wheel, (Leaves about a 100 grit finish...) on both the tight spots and to go back and finish the areas I used stripper on.
I'm sure that it's been suggested that you might want to do the work yourself. Not everyone has a level of confidence or the time to do so. Personally I did go the route of taking a class and completed much of the bodywork myself before time did become an issue. THEN, after all that work, I wasn't about to just "give-it-a-shot" and try laying the paint myself. I might later with another car but I spent a LOT of hours on this one and wanted a decent paint job that I didn't have time to go back and correct if it didn't end up as good as the substrate that I worked so hard to get done. With that I'll bring up another idea...
If money is an issue and you're looking for a nice driver, try outsourcing a local "just bodywork" guy. We had one here in our area and I've heard of craftsmen like him in other areas as well. They generally work out of their home or a small garage so they have lower overhead costs. THEN go to CARCOA or Maaco...I know, I know...Many shudder at the thought. But remember, it's the prep thats the key. Take that part of the equation out of their hands. It's been said that anyone can paint. That's not always true, but if you find a painter at the quicky places that's been doing it for awhile, (AND before being recruited by a more reputable shop!) you're probably going to get a decent job. You have to remember...These places survive on volume. These painters do as many cars in a week as a painter in a better shop does in a month. Next, insist on a more quality paint. The cheaper in-house paint or Nason brand that these guys use at Maaco etc. doesn't hold up well...especially reds. Ask for OR buy Sherman-Williams in the least...or go with PPG better yet. (If cost is an issue I doubt that Sikkens or House Of color is a consideration...) Also, insist...and pay for...2-3 coats of basecoat and at least 3 if not 4 coats of clear. THEN shop around for a shop that will colorsand and buff. I've found very good shops that will do a car for 3-400 dollars. It makes a $1000 paint job look like a $2500 one IF the bodywork was done well. One last thing...
Even an $800 white paint job will usually look better than a $1600 black one. So much more prep must be taken to make a dark color look good. Even if you can find it in the budget to do so, remember you have to live with it. Keeping a dark color clean, especially black, isn't as hard to do as some will have you believe. But keeping it up is another story. Every scratch, ding and dent is greatly magnified over your white, yellows, light blues & greens, etc. Not so bad if you never drive it or just on weekends. But if it's driven with any regularity......
AND speaking of living with it...Dark is hot. Not in a "cool" way...But in a "can't breathe" and "takes the skin off the back of your thighs" kinda' hot. And you would be surprised at how many people don't think of that. Not quite so bad if you have a light colored interior and/or AC. But black-on-black-on-black here in Southern California and in many parts of the country would be downright sadistic in July through September as a daily or frequent driver.
I realize that some of what I have said doesn't aply to your queery. But I thought it might be useful to others. When I was working at a Ford resto shop we ran the gammet of budgets. From hard working kids that wanted to be proud of their cars on a beer budget to customers that thought nothing of a 50 to 100k dollar (or better) coat of paint. (The F100 that won "Best of Show" at the Oakland Roadster show a couple years ago was done right around the corner from us...Cost? $150,000 just for the paint and prep.)
Most people can't afford a $5000 paint job. A lot can't budget over a grand. Many of the suggestions I have made are for those somewhere in between. I got tired of seeing the faces of kids working 2 jobs after school to afford one of these cars only to see their hard earned money go to waste on an ill-thoughtout paint job. It IS possible to get decent results on a budget as long as you know you can't expect Memphis BBQ quality ribs at the "Golden Arches". Jus' my 2 centavos......