For starters, I'd advise to learn more. Get a book like "Understanding Exposure" by Bryan Peterson. Google Zone System and learn how it applies to digital photography. The fact that you say you tend toward Aperture Priority tells me that you're not yet understanding exposure and how to apply it. Beginners that never really get out of the beginner status seem to use aperture priority the most.
Aperture priority is for when setting the aperture first is the most important thing. That would be depth of field mostly. Shutter priority is for when setting the shutter speed is the "priority." Hence the term priority. Shutter priority would be stopping action mostly. Using the wrong one can still be done, obviously, by watching the other as you change the wrong one, but that really makes little sense. It just shows that one hasn't mastered it yet. Program mode might be for those times where you really don't have a priority. Then there's us oldtimers who just don't trust the meter so shoot manually most of the time.
After you've learned basic Zone System and memorized full stops, it's time to start really understanding depth of field and how to isolate your subject. That 35 f/1.8 is a killer lens, IMO. There's no excuse for not getting wall hangers if you do your part. Moreover that D5000 is also a wonderful camera. My gal does wonderful with it. Start out by using one center focus point. Try turning the rest off for now and learning this. Learn to half press the shutter allowing focus on what you want to be in focus. Keep the shutter half down and recompose to put that place where you want it, and then press the shutter all the way down. On a portrait, I'd pick the eye that's closest to you or either if they're head on. Once in focus, put that eye at a to one side, maybe toward the light a little or whatever. Press the shutter the rest of the way.
The same would go for any other shot. Pick your target, half press, recompose and shoot. Just for fun, you might try spot metering while you're about it to get a hang of knowing what you're metering on.
I like to meter grass or something green in Aperture priority if that's important or shutter priority if that's important, then set the camera to manual with those settings. Now anything in the same light as that green grass will have a good exposure. Stopping movement for me is generally most important more times than depth of field. So I decide what shutter speed I want and let the camera tell me the aperture. I set that manually and maybe adjust based on a test shot and the histogram. Google how to use a histogram too. That and the Zone System will have ou shooting like a pro in no time. Bryan Peterson will teach how to apply it to your composition.
Forgot to mention, if you don't have green grass or a bush, you can meter off your palm and open one full stop to be the same as grass. Remember, your hand must be in the same light as your subject. The hand is zone 6 or twice as bright as a neutral density grey card. Grass is generall the same as a neutral density card. Saves carrying a card around or an incident meter. If your subject is in bright light, but the front of that subject is shady, hold your hand the same way. Think about the light and where it's coming from. For example, a bird in a bright sky right overhead is probably showing it's shady side to you, so meter your hand or grass in the shade. The light is all important. You're painting with it.
Once you set your camera this way manually, you need not change anything to do with exposure unless the light changes. For example, you're shooting a car race. You've found the right exposure by metering some grass in the sun. You've taken a test shot or so and adjusted for some blown hightlights. Now the camera is ready. You might not need to change the manual exposure setting for the next few hours. Just check occasionally. You're much faster and more accurate than letting the meter get fooled by reflections and sky. Just check that histogram every so often.
I"d glue that 35 f/1.8 on your camera until you've totally mastered it and the camera, then branch out. Take the protective filter off.
Sorry for the long post and the above is purely my opinion. Others might be different..
Edit: Visit the Grand Tetons. They are beautiful, especially after a Spring snowfall.
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Cheers, Craig
Equipment in Plan via Profile