I'm fairly new to the Star Trek universe as well. Its a great time to be into the novels. The universe is going strong, with some really great series, and a talented group of writers. When I started reading I was amazed at how cohesive the universe was between books!
Just to throw out my own recommendation, Check out "Articles of the Federation." Not only a great Star Trek book, but one of the best novels I've read in a long time!