New 1967 Barracuda Owner!
Great car! I have a 67 also.
Here's some of the lay of the land as far as suspension and wheels.
Your car like all pre-73 mopars has a small 4" 5x4 bolt circle which is a relatively rare size in wheels these days. Original stock options include steel wheels with full covers or dog dishes, as well as rallye wheels with caps and rings. Magnum or road wheels are another stock option (you can look all these names up). dog dishes on body color painted steel wheels with no trim rings is a very vintage muscle look (even more with repro redline tires whoo!!) .
As far as aftermarket mag wheels, the choices which are period-correct to my mind include slots, which it has now and which are by far easiest mag to find. (For all mags including these make sure the correct lug nuts are used to mount them, I'd check that on your car now especially if the wheels were added to help sell the car and haven't had extensive mileage.) Other great classic mags include Cragars, Torqthrusts, and Centerlines - these are the brand names, there are also similar made by other makers. This accounts for 90% of period mags you'll find, there are a few oddballs out there aside from modern styled wheels which to my mind look wrong on a late sixties car.
You have 14" wheels, which can be tricky to find tires for, but there are almost no 15" 5x4 aftermarket wheels, they are quite uncommon.
This bring the option of swapping to a larger bolt circle, to the 73-up 4.5" bolt circle. This means swapping both the rear end (or having axles drilled) as well as swapping to newer front hubs, which require also swapping the spindle and newer upper control arm which use a larger upper ball joint.
A really common swap, mentioned above, is to swap the entire 73-up disc brakes out of a later a-body. This gives you the larger 5x41/2" bolt circle plus the later single-piston disc brakes which are rugged and effective - the down side of them is that they're large and heavy, and many mag wheels don't fit over them without considerable grinding mods to the calipers. Larger bolt circle does open up more wheel options though.
Another option for stock disc brakes is the period dual piston Kelsey-Hayes discs, which work well and fit some mags better, they do have the small 5x4" pattern, down side is they're rare and expensive. There are also aftermarket disc setups including Scarebird, which uses the stock drum brake spindles.
I want to also point out that while the old 9" drums are barely adequate in perfect condition, the 10" drums are not bad in a a-body, and they are considerably lighter than most disc brakes, so an option for mild street use is just maintain your 10" drums, adjust them and use a shoe with a good modern lining. Trucks use drum brakes and have huge stopping power, so drum brakes are not the automatic liability people assume (though they do fade, which is an issue if you live int he mountains).
One upgrade you should absolutely consider no matter what brakes you run, is upgrade your master cylinder to a dual cylinder by swapping the MC for a dual one and the splitter block to a later mopar distribution block. With the single MC if any one of your wheel cylinders blows, you lose brakes entirely - with dual you only lose half, a huge difference in safety. There are numerous sources, I recommend the ones Ehrenberg sells on ebay as he also has the right fittings to adapt the MC to the line fittings you'll need.
As far as suspension, a-body mopars all have torsion bar front springs which are easy to swap and upgrade, simply swapping a larger diameter bar. Stock bars all are a bit bouncy because that was the soft ride desired at the time; swapping one size up is a nice stiff sporty suspension (smallblock bars in a slant six car, bigblock bars in a smallblock car etc). More than that is quite harsh for street use but good for serious road racing.
Rear springs can also be replaced and upgraded to springs with more leafs, there are also springs which are higher or lower for racing weight transfer. Stock mopar leaf springs however are very well engineered, their uneven chords acting like a ladder bar already. Unless your springs are sagging or broken, or you want to race, stock original springs are fine although another leaf is a good idea - but you don't need aftermarket to get good street performance.
This is a running theme with mopars in general - with other brands to go faster you customize them, but to make a mopar faster you make it more like the factory engineered police and racing versions, and often some of the parts you need are already in place. (the analogy in modern brands is how a BMW is engineered for much higher performance and detuned for the street, while a Honda is engineered so that every component is already pushed to its max.) This means a very different approach to performance where you don't have to assume everything will have to be replaced. In many cases those other brands have to install ladder bars, coilovers, etc just to match stock mopar street levels of performance. (again, if you are planning to drop a 500+ HP motor in and run nine second quarter miles, it's a different story)
Swaybars are a good option, many hi-po mopars came with front swaybars, you can use originals or aftermarket swaybars from Addco. They are mounted to tabs on the lower control arms which can be easily welded on. Many larger cars also came with front and rear swaybars (wider, they don't fit an A-body). Here's the deal though - front and rear sway bars especially are good for two things - either for tuning for extremely hard cornering as in autocross, or else making a stock street car with both very soft suspension yet no body sway - exactly what's desired in a luxury car.
When I built my 65 Cuda's front end, I planned to mount a front sway bar, but I found the stiff bigblock bars in front eliminated so much body roll that I didnt' feel like I needed a swaybar on the street at all, so I left it off. This is pretty subjective, but what I'm saying is don't assume it needs one until you install the actual springs you plan to use, then re-evaluate. Also, if you do install front and rear swaybars both, be sure the front is heavier, stiffer - if the rear swaybar is stronger than the front swaybar (or worse, rear swaybar only) the car will oversteer dangerously. (I know, some people will say otherwise based on autocross applications, but in that case the very stiff front springs used acts as additional front anti-sway.)
That's the basic situation for upgrading suspension on your 67 Cuda, and that will help you interpret the many posts on the forums by people making these upgrades.