The type of pump you need isn't really a preference — it's decided by how deep your well is. Everything else (horsepower, price, brand) is a downstream choice.
A jet pump sits above ground — in a basement, a well house, or right next to the wellhead — and pulls water up by creating suction. Suction lift is limited by atmospheric pressure to roughly 25–28 feet in ideal conditions, and well contractors generally treat 25 feet as the practical ceiling. Past that depth, a jet pump simply can't reliably pull water, full stop. If your well is shallow, a jet pump is the cheaper, simpler, more accessible-for-service option — the whole pump is above ground, so there's nothing to pull out of the casing when it needs work.
Fit a jet pump with a deep-well ejector kit — a venturi assembly that goes down the well and pushes water up rather than relying on pure suction — and its working range stretches to roughly 90 feet, depending on the model. It's still an above-ground pump with all the serviceability that implies, at a moderate cost step up from a plain shallow jet pump. Past about 90 feet, though, even a converted jet pump runs out of runway.
A submersible pump is a sealed, waterproof unit that sits down inside the well casing itself, below the water line, and pushes water up rather than pulling it. Because it's not fighting suction limits, it works from shallow depths out to 400+ feet — which is why it's the default choice for the large majority of residential wells drilled in the last several decades, regardless of depth. The tradeoff is service access: replacing one means pulling the entire drop pipe and wire assembly out of the ground, which is real labor (see the cost calculator for how much depth adds).
Horsepower needs to match your well's yield (how many gallons per minute it can produce), your household's peak demand, and how deep the water has to travel. As a rough starting point, ½–¾ HP covers a typical single-family home on an average-depth well with normal fixture count; 1 HP and up generally shows up on deeper wells, larger homes, multiple bathrooms running simultaneously, or irrigation demand layered on top of household use. Undersizing starves the house at peak demand; oversizing short-cycles the pump and shortens its life. This is genuinely a job for a licensed well contractor who can pull your well's actual yield and static water level — horsepower is not a number to guess at.