Below is a (long) list of all the artefacts to be found in ME1650. However, probably the top starting unclaimed artefacts are: -
Ring of Wind- Agent +40. This is usually located on turn 1 and in someone's possession by turn 3. The Free Peoples have to make sure this doesn't fall into the hands of a Cloud Lord agent. The DS have to make sure it does.
Ring of Curufin- Agent +30. Like the ROW usually in someones possession by turn 3 or 4. Agent rank is the most important in the game so getting these two artefacts on the same side gives a definate advantage to the fortunate player.
Collohwesta - Stealth +25. A surprise to many this. Imagine a couple of Cloud Lord agents with ROW, Curufin, Collowesta (and if given by Dark Lts) Cloak of Dark Abyss. All of these can be in a Cloud Lord players hands by turn 5. Both agents would then be able to assassinate most Free characters with a fair degree of certainty. Still, to many it's a suprise to see it ranked ahead of....
Tinculin - Mage +40. Mage rank is the weakest of the 4 skills, thats why I relegate this artefact to 4th place. Nonetheless this is a powerful artefact you should go after quickly. Imagine Elrond with this!
Collar of Might - Mage +30. Another unclaimed Mage artefact that's very powerful. Usually gets located on turn 2 or 3 but the other 4 artefacts above are usually located first and a mad scramble ensues!
These 5 artefacts are Neutral aligned (anyone can use them) and unclaimed. If you get most of these for your team you have a distinct advantage!
It's worth pointing out that artefact values vary from game to game by +5/-5 points. Theoretically the Ring of Wind and Curufin could both be +35 Agent artefacts. Conversely, the ROW could be a +45 agent artefact.
It's also worth pointing out that some artefacts are not always given to the same characters at game start. Din Ohtar usually starts with the Ring of Binding but Akhorahil doesn't always start with the Amulet of Communing. It can be hit and miss really.