Restoring from time machine back up across different Mac OS's
I am now the proud owner of a mid-2015 15" Macbook Pro running OS X Sierra. My previous laptop is a late-2008 13" Macbook running OS X Mountain Lion (I know, I'm behind the times in terms of Mac OS).
My question is this: What is the best way to restore my data from my time machine backups onto the new machine? My current time machine backups are centered around an older OS, so I'd like to lay out a way forward before I actually do anything. For example, should I install Mountain Lion on the new Macbook Pro first, restore via time machine, and then update to Sierra?
Thanks in advance for the help!