Josh, get a nice circular polarizer and a lens hood. Don't use a UV filter for your digital camera for landscape shots. As you said, your lenses are generic so its not like you're protecting a lot anyway. Keep your ISO set as low as possible and stop your lens down to f/5.6-8 in aperture priority mode.
Keep in mind that since the T3 is an APS-C camera that all of your focal lengths will have a cropped 1.6x view. So if you're using a 50mm focal length you need to multiply it times 1.6 so it will have an effective 80mm perspective.
I've found that lying to my viewers usually produces the most interesting landscape shots. Stuff from 17-35mm and again from 70mm on up (full frame equivalent) tends to either elongate or compress perspective--exaggerating the view of what you normally see. 50mm focal length usually looks boring because its how we normally see. Be aware that using a circular polarizer at ultra wide angles will usually result in uneven banding across your sky because its capturing both the polarized angle of the sun as well as the non polarized angle. Doesn't matter whether you paid $100 or $1,000 for your lens, they'll both do this.
