That's a nice H1 Steve, well done! Is the 2 stroke oil pump working? If you're not sure, it's best to fill it with premixed 2 stroke fuel for the first start up, the last thing you want to do is seize the engine and burn your bearings.
I rode a H1 back in the mid 1980's (my mate Davey bought one in mint condition like yours) and it was a wicked little beast, quicker than my K1, but felt very "loose" in the twisties. Not life threatening, but not as tight as say, your RD.
Have fun on that thing, they were a game changer for Kawasaki, and a piece of motorcycling history. Cheers, Terry.