The 50mm f/1.8 is a nice lens for the price but it has it's limitations.
The problems I have with my 50mm f/1.8 are:
It has extremely slow auto-focus, especially in low-ish light (like indoors) - to the point it's hard to catch kids running around, not a problem for portraits but it's difficult to use it on anything that is moving unexpectedly (if you can't prepare and pre-focus).
50mm on an APS-C camera (like the 60D) is a little too tight for general indoor use for my taste, great for head and shoulders portraits but you will find yourself limited by room size for full length and group shots (meaning you are limited in where you stand and where you put your subject, you lose a lot of control if you always need to place the subjects right next to a wall), also, it's practically useless to capture the atmosphere of the entire room (unless you can stage everything or you are very good at framing your shots).
50mm is also too wide for things that are traditionally shot with a tele lens - forget sports, forget wildlife (also forget animals at the zoo unless the poor animals are in a bad zoo with really small cages), etc.
I recommend getting a kit zoom at well as the 50mm, they aren't the best lenses ever made but they are good enough for a hobbyist and are very versatile, you can get the 18-55 for cheap with the camera or for next to nothing used, the 18-135 is better if you have the budget.
If I want to take a staged portrait I go for the 50mm, but as a general walkabout lens I use the 18-135 and most days the 50mm stays in the bag (I know preferring a consumer zoom over a prime makes me an horrible person or something but the fast auto-focus and extra reach of the zoom lets me easily take pictures I wouldn't be able to take with the 50mm).