Im currently remaking a v4.6.1 site that's being rewritten in 6.1.x.
We're supposed to migrate all the data from the old site into the new. 

I need to move Contents and Media.
Also, i dont want to move the complete structure, and also the docuement types aren't the same.
... meaning i need to select parts of the structure and map some properties between the two sites. However, it isn't vital that the structure of the Media is kept as is.

What would be the best aproach doing that?
What tool would be preferred?