I’m getting a 45 W solar panel kit ( http://www.harborfreight.com/cpi/ctaf/displayitem.taf?Itemnumber=90599 ) for a greenhouse. I want to have a small heater in case of freezing temperatures and a few lights. I’m in the Willamette Valley, Oregon.
I wanted to know approximately what kind of batteries and how many I should get.

You just get the standard 12 volt deep cycle marine batteries. Any auto parts store should have them. The problem is that you want to run a heater. When heaters need on average 1500 watts and your charger is only 45 watts. I can’t give you specifics on how many batteries you need but its more than one. You should probably try two and see if that works OK for you.