Jw is correct you can install what is called a 320 meter base with double lugs. And in most cases inspectors will allow this in my experience by using the unlimited tap rule of NEC 240.92(c) 1-5 and NEC 240.21 (B)(5). The key here is the tap must be made outside the structure of the main dwelling in your case. So that pretty much leaves only the load side of the meter. I have seen split bolts used on the load side service entrance conductors but that to me just isnt the way to go.
You also have a another choice... you can install sub-feed lugs in your main panel. Here is a link to the installation of sub-feed lugs in a square d Homeline panel.
Remeber when you install these the feeder to the shop sub-panel must be rated equal in amps to the main disconnect in the house main panel. This is because the main panel disconnect (overcurrent device) is protecting the sub panel feeder at 200 amps. The sub-feed lugs are not an overcurrent device merely a tap device. You will also need a neutral lug kit to install on the neutral bar of the main panel to accomodate the neutral going to the shop. You may also need to install a ground lug it will just depend. This is generally done by installing a ground bar in the house panel (there are predrilled holes for this) in the panel back and terminating the ground wire to the shop (if required) to that ground bar or you can terminate it to the neutral bar since ground and neutral are bonded there. Most will take up to a #4 awg wire. In your case if your main breaker or disconnect is 200 amps at the house panel then you will need a minimum #6 awg insulated copper ground wire or a #4 awg aluminum ground wire.
Now the determination of whether you need a 3 wire feed or 4 wire feed depends on two things....what local code requires for a new installation and if any metalic paths other than the sub-panel feeder connect between the house structure and the shop.... ig...water lines , phone/ data line... etc. If any metallic paths will exist in addition to the feeder then a 4 wire feeder is required. then of course if local code requires a 4 wire feeder. If neither then you may run a three wire feeder.
So if a 3 wire (H-H-N) is run then the neutral and ground remain bonded in the sub-panel. This is done commonly with a green bonding screw that fastens through the neutral bar and threads into the metal can of the sub-panel bonding the metal. It will vary from manufacturer as to what they use to bond the metal of the enclosure to the grounded conductor (neutral).
If 4 wires (H-H-N-Grd) are required then the neutral and ground are seperated electrically in the sub-panel. You will generally have to purchase a seperate ground bar for the sub-panel and install it to the swaged pre-drilled holes in the panel back. You will not
install the bonding means such as the green screw or other method. the feeder ground wire and all branch circuit ground wires will connect to the ground bar and all white neutrals will atttach to the neutral bar that came with the sub-panel. In some cases the panel will come with the extra ground bar. Just make sure the bonding means isn't installed.
Here is a link to some information on what you are doing....read the first part then scroll thru the pictorial examples till you see the installations for a 240 volt underground supply for 3 and 4 wire feeders. Hope this helps... there is a lot to know with your project as you can see.
As for the type of wire if going underground as a lateral feed in conduit then thwn rated copper or al as Jw mentioned. You can also buy USE-2 which is direct bury and can enter buildings. This use-2 is also rated rhw-2 and rhh-2 in most cases. Remember if you opt for aluminum it will be 2 sizes larger than copper to provide the same amps generally and this will also effect your conduit size that is required to stay at 40% fill. In your case it gets bigger for both copper and al because we are having to keep voltage drop limited at that distance.
Continue to ask your questions I'm sure there will be plenty.