Rear end for 65 barracuda with 5x4.5 bolt pattern

The Mopar 8 3/4" is a great axle but is not cheap in factory form.
An 8 1/4" axle is a great choice as it will have the right bolt pattern that you want but many have either a 2.45 or 2.71 ratios, not much gear for a car if you want to have good off the line acceleration. Once you swap gears into one, "budget" goes out the window.
The Jeep Cherokee, Liberty or Ford Explorer axles require some welding but they have great gears and often have a limited slip differential and disc brakes. You can find them at self serve wrecking yards for under $200 on their discount weekend sales events.