Does mining need a special electrical circuit or outlet?

For a typical home rig, no. A standard household outlet on a normal 15A or 20A circuit comfortably handles a single PC drawing a few hundred watts - the same outlet you would use for a vacuum cleaner or kettle. A 400W rig on a 120V circuit pulls about 3.3A, a small fraction of the circuit's capacity. Caution is only needed for unusually large multi-GPU rigs, or if you run several rigs plus other heavy appliances on one circuit, where the total can approach the breaker limit. Never daisy-chain rigs through under-rated extension leads or cheap power strips. If you are unsure about a big setup, have an electrician confirm the circuit rating; for one ordinary PC, you are fine.