Designing a Teleportation device, you first have to decide if it is a "Push" (with "Receiver" AC target) or "Pull" (with "Sender" AC target) item. Both have advantages and disadvantages.
A "Push" item is going to be lower level because it only needs a Range of Touch. This makes it 15 levels lower which is easier to enchant and takes less Vis. However it must be at the site and cannot penetrate AotH (well it can with enough Penetration but not worth it compared to "Pull"). This means it is easier to steal and the receiver has to be outside of the Covenant AotH.
A "Pull" item will be within the Covenant which makes it harder to steal. Being enchanted in the Covenant and present during the annual AotH lets it function through the AotH. However it will need the AC Range which makes it 15 levels higher, thus more difficult and expensive to enchant.
For the Target it depends on how much you want to potentially send at once.
Individual really needs some sort of "sighting" effect to make sure you get what you want unless you are OK with pulling a single random item if there are multiple possibles. If someone put a mix of items in the "Sender" box every time the effect was activated a random one would be sent.
Group is OK since generally all of the stones that could be placed in the "Sender" would be less than its maximum of 10x Base Individual. However if precious metals or gemstones were placed in the "Sender" then you could easily exceed its maximum. Only use if Room is not a valid Target.
Room is better than Group in every way for the same cost. A closable box is also a valid Target for Room. So if you are going with boxes use this one.
The Base for Transporting non-living objects an AC distance is ReTe Base 25. It requires Requisites for things primarily not covered by Terram (teleporting dead plants is ReTe(He) rather than ReHe). Note that this does not require the additional Mags a ReTe effect normally would to effect things other than earth (Stone is a +1 for control). So unless it was restricted to just stones, it could be used to send dirt, metals, and gems as well.
As the Fixer calculated, the level for a "Push" item would be 40. With the need for an AC Range, the level for a "Pull" item would be 55.
If your Magi lack sufficient ability to craft a "Pull" item themselves, I would recommend going with a "Push" one. A "Pull" needs to meet specific requirements to function and if you hired the work out then it would have to sit unusable for a while.
EDIT: Forgot the whole "is Vim needed" thing. It should not be, since you are moving the object rather than transferring the vis from one physical object to the other. However it does present another option rather than teleporting the rocks.
You could go with a ReVi Base 10, AC Range Effect to move the actual Vis from the stones in one box to something at the other end. There is no difference in the level of a Push or Pull design here, which means a Pull design is better.
There is a "slight drawback" in that all the vis will be put into a single object, without some extra design work and use limitations. However it is pretty easy to split it up if desired (common low level spell/effect) so not really much of an issue.