When to use different image sizing options

It is important to understand a fundemental function of the Resize 'dimensions' effects-

ie. If you enter 'W and H' , then you are defining a virtual "box" that the exported image must fit within, whatever its ratio of W:H.

In my screen-clip, with W1920px x H1080px defined for the resize, you might see how a Vertical (Portrait image) might export 1080px High.

A square 1:1 ratio image would export at 1080px x 1080px,  a panorama at W1920 x H??

"Long edge/short edge" mean just what they say, and a photo of any crop ratio will export with the defined dimension. eg. a Vertical (Portrait image) with a resize to 1920px Long edge, would export at 1920pixels high.

"putting images on the web" may require you to define various Pixel dimensions, as recommended by the intended sites. (eg. 800x600pixels).

A "Megapixel" limit will attempt to compress a JPG with a quality automatically chosen to achieve the limit. Sometimes if you export at original 'Full-Size' pixels, LrC will give an error as it may not be able to compress the 'full-size' pixel count to meet the megapixel limit.

Digital images are made up of pixels, and don't have physical dimensions.

The PPI value is used to determine printed size. PPI stands for Pixels Per Inch, and is optional metadata.

Pixel dimensions divided by PPI value = Printed dimensions in inches.

For instance, an image with the pixel dimensions 2400 x 3000 with the PPI value set to 300 will print at 8 x 10 inches.

For screen viewing, PPI is irrelevant, the image will display according to its pixel dimensions, regardless of the PPI value.

So, if the exported image is intended for screen viewing, export in pixels.

I nearly always use Long edge, the short edge is then automatically calculated.

I have never had any need to use any other options than Long edge and Short edge.

If the image is for printing,  choose physical dimensions, and Lightroom will do the math for you.

This may give you the impression that the image has physical dimensions, but under the hood, there are ony pixels and the PPi value.

I use Long edge for printing as well. 

Megapixels express the total pixel count in an image. A 6000 x 4000 image is 24 megapixels (24 million pixels).

I have never had any need to export using Megapixels.