Spearguns are powered one of two ways, and for most beginners in the US the choice leans one direction.
Band / rubber-powered
By far the most common style, and the one most experienced divers steer beginners toward. Bands (also called rubbers) are simple, quiet, and easy to maintain; you can tune power by adding or swapping bands; replacement bands are cheap and available everywhere; and the guns tend to be buoyant. The trade-off is loading — you brace the butt against your hip and stretch the bands by hand, which takes some technique and effort, especially on longer guns.
Pneumatic / air-powered
Air-powered guns are compact for their power and popular in the Mediterranean and among some cave and reef divers. The upsides are a short barrel for a given power level and a very direct feel. The downsides for a first-timer: a louder shot, more complex sealed internals, maintenance that's harder to do yourself, and the need to pump/charge the gun. They're capable weapons in the right hands, but they're a steeper on-ramp.
Bottom line: unless you already have a reason to go pneumatic, a band-powered gun is the starting point. This isn't a soft preference — when beginners ask the spearfishing community, the standing advice is blunt: get a band gun first, "no pneumatic." Bands are simpler to own, cheaper to keep running, and far easier to get parts and help for; pneumatics earn their keep later, in niche cold, murky, or tight-quarters diving.