You sound like a student on a tight budget, so yes an inexpensive prime such as the 50/1.8 might be a useful lens to experiment with. Be aware though that on your camera this is a short telephoto lens. Very appropriate for portraits, perhaps, but possibly a little limited in its scope. A street shooter, for example, might want a more "normal" to moderately "wide" lens, which would be 30, 28, or 24mm to around 20, 18mm or so, on your camera. A wildlife or sports shooter would generally want more powerful telephotos, 135mm and longer on your camera. You actually already have these focal lengths with your zoom, altho a bit limited on both the wide and telephoto ends. But you can experiment with them.
Most SLR shooters don't "make do" with a single lens, zoom or prime. That would sort of defeat the purpose of an interchangeable lens SLR camera. The whole point of an SLR is the ability to fit a lens that's most appropriate for a particular type of photography, as needed. Of course, you have to have first some idea what you want to shoot and how you want to shoot it!
It sounds as if, although you have some movie/video experience, you have more basic learnin' to do about still photography.
First, learn to use the camera's AF. There are a number of things you can do, if you aren't already. Step one is to stop using All Points AF. That just leaves it up to the camera to choose the point of focus. I recommend scaling back to using a single point, manually selected. Often the center point is the best, since it generally has additional sensitivity compared to the other points. But don't be afraid to use other focus points when needed, individually selected so that you are in charge of where the camera focuses.
Use AI Servo for moving subjects (also works for non-moving subjects), One Shot for non-moving subjects with a higher degree of accuracy. You can set the camera to give you focus confirmation with One Shot... flashing the green LED in the viewfinder and/or giving you a "beep". Forget about AI Focus, which is supposed to decide for you whether or not the subject is moving, then choose one of the other two focusing modes. It's slower to respond, in my experience.
You also have some other focusing options, with that cool articulated LED on the 60D and Live View. I don't use them enought to really advise, so check the manual.
You also might want to set the viewfinder diopter to your vision. Easiest way is to remove the lens, hold the camera in front of your computer (with a plain white document of something) or another evenly illuminating light source, then dial the diopter + or - until the AF boxes in the viewfinder appear as sharp as possible. This should correct for any failings of your current eyeglass prescription, when taking the photos. This won't help you when viewing those images later on your computer monitor, though.
Personally, I also use "back button focusing" which you can find more info about here on POTN with a search, if you wish. Canon also has info about using this method on their website. Mainly, "thumb" focusing separates the AF function from the shutter release button. It's an old Canon sports shooter technique, but certainly isn't limited to just sports photographers and largely eliminates focus errors that happen when using single point and not always composing with the subject precisely in the center of the viewfinder. With AI Servo you can do maintain focus on moving targets by holding the button down with your thumb continuously... before, during and after exposure(s). With One Shot, you can just press the button until you hear or see confirmation, then lift off the button and focus will stay where it is (actually you can do the same with AI Servo, but you don't get the confirmation and it might not be quite as precise as One Shot). Check it out, if you want to give it a try. It only takes a short time to get used to, becomes second nature to focus this way quickly and puts you in full control of the point of focus. It's similar to manual focus in some respects, but faster and more accurate than I ever was manually focusing my lenses!
I'd also suggest you get some books and study them. In addition to the manual you got with your camera, one of the third party guide books such as the Magic Lantern series, that are specific to the camera model, can be very helpful. These sort of pick up where the manual leaves off.
"Understanding Exposure" by Bryan Peterson is another book I'd highly recommend. It really should be on the "must read" list of every modern SLR user.
There are books about specific types of photography that give a lot more good info about lens choices. But you first need to know what you want to shoot.
I don't have the 18-135, so really can't comment about that particular lens. However, I bet like most lenses that it has a "sweet spot" aperture where it gives sharpest images. I'd suggest trying f5.6 or f8, to see how those work for you. You might be able to improve your results with it by adding a lens hood and, if you have one fitted, removing any "protective" filter and leaving it off until it's actually needed.
18-135 is a pretty nice range of focal lengths. It covers the all the main focal lengths that most 35mm film film shooters ever owned in their lifetimes (equivalent on your crop sensor camera to approx. 28mm, 50mm, 70-210mm that were the most common lenses used by "full frame" film shooters in days gone by).
If you can't find anything to photograph, you aren't looking hard enough. I've never been anywhere that I couldn't find an interesting (to me) photographic subject within a few minutes of looking. Just keep looking! Don't be too quick to add a lens right now. Learn to get the best out of what you've got, then you'll prbably have a better idea what you actually need, to get the shots you want.
