This is often surprising to many, but complicated machines were not unknown in the ancient world. There were water-clocks (which functioned much like really big versions of modern clocks, and driven by water and gravity), and we hear scattered mentions of mechanical devices related to observing/predicting astronomical phenomena. The Antikythera device certainly belongs to this broad category of object, though it is (apparently) much more complicated than the average ancient mechanical device. Cicero, in Tusculan Disputations, makes mention of a sphaera of Archimedes (a device by which he "bound" the motions of the celestial bodies), though he is frustratingly vague.

In any case, the device of Archimedes, or the Antikythera, were not every-day objects. Those with specialized knowledge knew of their existence, and maybe even had seen one, but you couldn't go down to the forum of your local municipium and pick one up. The Antikythera device was incredibly expensive, as you suspect.

We know a few things: because of its obvious value, it was probably not on the ship as cargo. Jones (Portable Cosmos 2017) supposes the device was newly-created and on its way to its new owner in the company of a caretaker or "technician." We don't know if this person survived, but likely not--whoever paid for the device certainly had the resources to retrieve it from the wreck, which wasn't in excessively deep water. Greek sponge-divers were able to discover the wreck and pull up its treasures 2000 years later without any equipment. We know the ship contained goods of many varieties, as was typical on a large merchant vessel (40+ feet). It had amphorae of wine, bronze and marble statuary, glass, and other luxury items, all probably manufactured in the eastern Mediterranean. The big ship was probably originating from a big port, like Delos or Ephesus (there is strong evidence for Ephesus); and the ship was clearly headed west towards Italy when it sank in the narrows between Crete and the Peloponnese, near the tiny island of Antikythera, around 60 BCE.

The intended owner, who- or wherever he was, was almost certainly rich, but that doesn't narrow things down very much. There were lots of rich Romans. The owner probably had knowledge of some kind related to the device, either because he had seen one in person or had heard one described by a rich friend. Roman aristocrats were frequently educated in the Greek east in the first century BCE and would have had many opportunities to encounter such a device. Early in the discovery it was supposed that the ship captain owned the thing, and that it was a navigational tool, but that is 100% debunked now. The device can help with navigation, but it does so so so much more. Only about half of the many read-outs from the device would pertain directly to navigating the sea. In fact, the variety and sheer number of the read-outs/displays suggests (to me at least) that it was an object of scientific curiosity first, and of practicality second. The sort of data which this device imparts was available from elsewhere, in non-mechanical form. You could go to a professional astronomer, pay him a steep fee, and he could consult his ephemeris -- a pile of charts and scrolls with the same information as the device, just not nearly as cool. The device seems to have been, simply put, something like a mechanical soldier, only not a soldier but instead an astronomer.

so:

rich: yes, very

someone in the astronomical profession: probably not

experience with scientific topics: probably

where?: presumably in the west, either Italy or further west; in 60 BCE, Rome seems the obvious best guess to me based on the wreck's position and apparent direction

Check out Jones' book. Very easy read and has a nice summary of the discovery, the century of investigation, and does a good job of contextualizing the device in the ancient world.