Kerosine,
The 737-300 is a very stable machine and if the sim is a reasonable one then the handflying should be fairly straight forward. Its a while since I flew the 737 but from memory it is good not to overtrim. When I say that I mean don't hold down the trim switch waiting for it to feel right. I found it easiest with a change of configuration to give it a few blips on the trim then assess. Like most big jets using the datum thrust settings vs pitch attitudes makes life much easier. Hopefully someone more current will give you those or maybe the assessing company already has.
Good luck!