I'm going to similarly omit a neckline that I never use: the boat neck. It's essentially a horizontal slit at the shoulders big enough to admit the head. It doesn't fit well, shows bra straps, and slides around on the shoulders. It is the easiest of necklines to design, and so many beginner knitting patterns include it.
My advice: don't waste your time on drop-shoulder sweaters and boat necks. If you're going to put all those hours of your life into a sweater, make it a sweater that will fit and flatter the wearer.
For necklines, you have three basic choices: round, square, or triangular.
A square neckline is usually a poor choice for knits. Knit garments tend to stretch, and a square neck tends to bag and sag. Knit fabric does not have the crispness of woven fabric that makes a square neck a fine choice for many garments. You can sometimes get away with a square neckline in a lightweight, stiff, nonresilient (or very springy) yarn knit at a firm tension and edged with a slip-stitch, twisted stitch, or crocheted edging. Conversely, you can use a square neck in a very drapy fabric that makes the sagging and bagging a feature. In most cases, however, a square neckline in a handknit garment is a disappointment.
A round neckline is a much better utility player. Here the characteristics of knit fabric work harmoniously with the shape of the neckline. The stretchiness and forgivingness of knitting smooths over any irregularities in the round edge. Round necklines can be wide, narrow, high, or low. A high, narrow round neckline is the classic crew neck. A high, wide neckline is a portrait neckline. A low round neckline, whether wide or narrow, is a scoop neckline. All of these necklines work great for knit garments.
The triangular neckline also works well for knit garments. These appear as short sharp triangles in the classic V-neck sweater or as the long, graceful shawl collar in a garment that opens in the front.
When planning a neckline, you can either copy a neckline from a garment or pattern that you like or you can wing it from your measurements. Both methods work well.
For many years, my neckline placement was often surprising. I copied and measured, and the necklines were often inches shorter than I expected them to be. The fronts of my sweaters rode up.
What I didn't realize was that sweaters hung from the backs of my shoulders, not the middle of my shoulders. The front of the sweater thus started close to the back of my neck, rotating the neck of the sweater back and up.
To find your own hanger point, hang a towel over your shoulders. and feel for the line where the towel hangs. Measure your necklines from that line, and the depth will be close to right.
Another thing to think of when planning necklines is the width of the neckline trim. The neckline of the initial garment needs to be deeper and wider than the neckline of the finished garment in order to allow for the neckline trim.
If you're copying a neckline from an existing garment, measure the width of the neckline at the shoulders, the depth of the neckline, and the width of the neckline at the deepest point. Choose the shape of your neckline, and proceed as if designing the neckline from scratch.
If you're designing the neckline from scratch, choose the neckline width at the shoulders, the depth of the neckline, and the width of the neckline at the deepest point. Settle on a neckline shape, and you're good to go. You can use a string or ribbon around the neck to try various neckline shapes before taking your measurements.
In top-down sweaters, the neckline is shaped with increases at the left and right edges of the neckline. The total number of increases is equal to the stitch gauge of the knitted fabric times the width of the neckline at the shoulders. The depth of the neckline times the row gauge gives you the number of rows to space these increases across.
For a triangular neckline, the increases are spaced equally across the rows. Don't worry if the math on this (or any other aspect of knitting) doesn't come out even; just use the nearest whole numbers that make sense.
For a round neckline, the increases occur more frequently as you go down. For about a quarter of the depth, you don't increase at all. For the second quarter of the depth, you increase every fourth row. For the third quarter, you step it up to every other row, and then step it up again to every row for the last quarter. The final group of stitches are then cast on at the bottom of the neck. You'll need to adjust these sections so the number of stitches come out right, but what you're looking for is a progression in increases from the shoulder to the deepest part of the neck.
Faking it is a major part of sweater design. Get the numbers somewhere in the neighborhood of where you want to be and then juggle things so they work with the stitch pattern and the stitch and row gauge.