When I first bought my camera, a Nikon D3200, I had somewhat of an understanding or what I was getting with a CMOS or cropped sensor versus going with a more expensive full-frame sensor camera. A smaller sensor generally means that 1) the low-light performance of that camera won't be as good as the more expensive cameras that have a full-frame, 2) there are not as many lenses to choose from that are specifically built for your sensor, and 3) many of the most popular lenses are made for a full-frame sensor and do not behave the same when used with a cropped sensor.
These three points may seem like major negatives, but they really are not. It's all a matter of working with what you have. It's possible to produce great professional looking images with pretty much any modern day camera and this includes cell phones. A quick web search on "phonography" will show you what I mean. Also consumer level cameras are now more capable than what was considered professional grade a few years ago.
Fast glass is a great way to improve any camera's low-light performance. In this case if you were trying to save money when you initially bought the camera body you will need to cough up whatever you saved to purchase a good lens or two. Typically you're looking at a lens that has an aperture of F/1.8 to 1.2, though 2.8 is good. In the video series that I posted in part 1 of this topic Tony Northrup says something that I agree with. These high megapixel cropped sensors require a lens that is capable of achieving a wide aperture. This is just necessary to ensure that the sensor is bathed in the proper amount of light to produce the best images. This is something you generally don't get with a kit lens, a lens that's sold with the camera body.
Speaking of lenses, Canon and Nikon don't seem to be in the business of providing a wide variety of lenses for the cropped sensor camera bodies that they produce. Thankfully Tokina, Tamron, and Sigma fill in the necessary gaps here. Lenses from these companies continue to get better. In the past the recommendation was to not go with a third party lens, but some of these companies, Sigma in particular, are producing lenses that rival those found from Canon and Nikon. These aforementioned companies are continuing to produce key lenses that cover the gamut of any photographer's shooting needs.
Despite the variety of lenses produced for a cropped sensor you may still desire a lens that's only been produced for a full-frame sensor. For example I desired to have Nikkor's 50 mm F/1.8 because of the great image quality it offers at a desirable price. And, yes, while this is an FX or full-frame lens and not created for a DX or CMOS sensor I bought it anyway. I was interested in the maximum aperture of this lens to help increase my ability to shoot in low-light situations.
On my Nikon D3200 this lens acts more like a 75 mm lens than a 50 mm. This means that I must be further away from my subject to fit everything I need to in a shot. I'm okay with this as I've gotten used to this and adjusted to it. This proved to be a great purchase as this lens produces some of the best and sharpest images out of all of the lenses that I own. So, don't be afraid of FX lenses on a DX body.