Cropping won't alter image quality unless you crop off the good bits.
Resizing always alters image quality to some degree. Let's say you were intending to create a 16x12 inch print at 300 dpi. Now if your photo just happened to be 16 x 300 pixels wide and 12 x 300 pixels deep, then you wouldn't need to resize it. But if your photo is any other size at all then the resize algorithm is going to have to guess the colour that each pixel should be, and that's where different algorithms produce different results. Photoshop Elements, for example, has five different algorithms you can choose from (Nearest Neighbor, Bilinear, Bicubic, Bicubic Smoother, and Bicubic Sharper). Lightroom only has one algorithm which one Adobe Community user describes as an "adaptive hybrid of bicubic smoother and bicubic sharper", which I assume is going to be better than choosing either of those algorithms in Elements or Photoshop.
One of the best resizing plugins often recommended on the web used to be known as Genuine Fractals and is now known as Perfect Resize, and you can get it from
OnOne Software but it works out less expensive to buy the entire
Perfect Photo Suite. I don't do a lot of resizing, but Perfect Resize has produced noticeably better results than anything else I've tried. If you do a lot of resizing, you might want to give it a try, using the "Free Trial" button. [Usual disclaimer: I have no relation with OnOne Software other than being a satisfied customer.]