Is there a cheap relay that can control voltage from stuff like bulb lights with a 5 V control output? I need to power a light bulb or something like 110 V or 220 V at normal amperage for TV or something at that range like a fan...

My micro-controller is an Arduino with 5 V out and 12 V max out trough transistor switch.

To my understanding a stepper motor drive could be a viable option to enable the relays... I can even control current, right?

Up to 8 channels

Could this work better?
You can use a 5V Solid-State Relay module to control light bulbs. They cost $4-6 from US-based suppliers and $1-3 from a Chinese supplier. Just hook up the supply to the center pin and the load to either the NO or NC pin. Supply 5V to the module and wire a digital pin to the module to control it.