I have 1GB RAM in my MacBook Pro 2.16GHz Core Duo 17", model number A1151.
I have one empty slot to insert 1 GB RAM. What type of memory do I need to buy?
In order to find out what type of meory you need, you should check out Apple's own support site:
You can then use the links at the top to find out more about your model (i.e. Late-2008 and earlier).
EveryMac.com also has a page for … well, every Mac, which then lists the type of memory used. You'll find it in the specification table. For your machine, this would be here.
They also have a FAQ site dedicated for the pre-unibody MacBook Pros:
Note that your MacBook "officially supports up to 3 GB with a 2 GB SO-DIMM in one slot and a 1 GB SO-DIMM in the other".