There are a lot of different opinions about how to set up a Lightroom catalog. Some teachers suggest creating a new catalog for each shoot, some say one new catalog for each year. After 7 years of working with students privately, I have to say - one catalog - is all you need, especially if you keep your Library photos and folders in order. And your Library should be on a dedicated external hard drive. And, if you're using a laptop, then Smart Previews are the way to go, as they allow you to edit and develop your photos without actually having the hard drive with you.
What's a Catalog and what's a Library?
The Lightroom catalog is how Lightroom knows where your photos are on your hard drive. It is also where it keeps all the information on what you've done - flags, rejects, developing, books, etc. Consider the Catalog a big filing system, but it's not a file cabinet. This is a unique aspect of how Lightroom works and can trip up many beginning users.
The Lightroom Library could be considered the file cabinet that is connected the Lightroom catalog filing system. The photos and folders on your hard drive are not inside the catalog, instead they are LINKED. Because of that, Lightroom can easily lose your photos if you make any changes from inside your Finder or Explorer - if you're on a PC.
The Catalog. Having just one catalog means you (and Lightroom!) always know where everything is. There's no guessing as to which catalog you put your summer vacation from 2012 or, where the photos are because they are all in one place.
The Library. If you import all your photos to Lightroom using a "master folder," that is a top level folder where everything you shoot gets imported, then your photos can easily stay in order. I recommend importing into dated folders, which you can later add a title to. Something like this: 2015-08-27 Brooklyn Bridge - This way all your photographs are in chronological order and you can create Collections later (another topic for another day) from your favorites so you don't have to move your photos away from their appointed location.
One Lightroom catalog and all your photos in one location with chronological folders on an external hard drive. It's a mouthful, but it's a successful formula for keeping organized!