For this kind of simple website product work, a hotshoe flash is the easier and more foolproof first buy.

A TTL speedlight can give you soft, even light with minimal setup: bounce it off a white ceiling, place the dummy in front of a plain wall, and you’ll get flatter, more flattering light with fewer hard shadows than direct flash or household lamps. It’s also more versatile as a general first lighting tool.

A studio kit is more useful if you specifically want more dramatic, angled, or sculpted lighting. But it will usually be more complex to use: you’ll need to work in manual mode, position lights carefully, set power levels, and sort out triggering. Depending on your camera, connecting and triggering studio lights may also be less straightforward.

So if your priority is quick, repeatable, reasonably good product photos as a beginner, start with a TTL hotshoe flash. If later you need more control over light shape and a more formal studio setup, then add studio lighting.