Having troubles with my (single pivot side-pull) brakes

I'm brand new to bicycling so pardon any terms that aren't right or stupid things I may say.

I just dug out my dad's old FreeSpirit road bike he bought from a big-box store back in the 80s to repair and ride around for recreation. I don't think it's a bad bike but some of the components on it are a bit outdated and cheap.

Brakes are giving me the most trouble right now. They're single-pivot side-pull brakes. Whenever I use the front brake, the left side caliper sticks to the rim and the brake handle doesn't reset itself. I have to get off my bike and pull the brake away from the rim manually. I've tried adjusting every which way and no luck. My back brakes are almost useless as well, no matter how I adjust them.

Should I invest in some higher quality, not so out-dated double-pivot side pull brakes, or is there another choice that people prefer for road bikes?