You should already have a 3/4" bar in a 390 Cougar. Small blocks came with 11/16".
Most of the aftermarket front sway bars are made to fit a small block, if you try to use them in a big block FE they hit the harmonic balancer when you hit bumps. Looks cool if you are in a car next to the one with the problem, shoots sparks from under the front of the car like sparklers! It ruins the sway bar pretty quickly, cuts a semi-circular notch into it. Other bars hit the oil filter on big blocks.
Addco makes some better quality front sway bars that will clear. You also might try to find one from a '69 or '70 428 Eliminator, they are15/16ths diameter. I would go no bigger than 1" unless you are autocrossing.
Rear bars are all OK from any of the vendors. Addco makes adjustable ones which are pricey. Again the stock Eliminator or Mustang Boss 302 bars show up at swap meets and on EBAY and fit great.