About that, conduit. This isn't just a direct bury?

 

It's gotta be classified for for underground...

Either electrical PVC or uf...underground feeder

 

PJ

You're far better off running your wire in conduit. Run it in schedule 40 PVC and get a generous size. Get some long sweep 90s too, and run schedule 80 where it is above ground. You can also buy a large spool of single conductor wire and cut into three pieces. Don't worry about it being the same color as you can identify the conductors and mark them with white, black and red tape after the pull.

You also only need three conductors because you can drive two ground rods at the new panel. Drive them 6 feet apart and connect them to the panel with one continuous piece of copper.

Just look at some ampacity charts for your wire size, this is not rocket science. But I would also go one size larger for every 100 feet and I'd definately run aluminum because it's far cheaper and just as good as copper for main feed wires. The larger size means less voltage drop under heavy load and also less energy lost to heat.

A larger panel is a good idea because you can easily add more breakers later, but it also means larger feed wires.