Over the years I've made a fair number of ugly bowls. Initially the problems were related to poor technique, but once that was sorted I was left with the ones that were just ugly by design. With each bowl I turned, I took the time to analyze what I liked and what I didn't, and tried to determine what I could have done to make them better. Eventually, I figured out a few simple rules that work for me. Other people's tastes will differ, of course. It's a journey and its all about self-expression, so have fun with it. From firewood it came, so no harm in making more firewood!
Bowl aesthetics are very personal. Golden ratio proportions (e.g., ~ 3:5) are a great place to start, but don't let it lock you in. I like bowls that have a height to width ratio of 3:5, but 2:5 is also nice and 1:3 makes sense for a functional bowl vs. a decorative bowl. Vases, being more elongated, have different rules. I prefer a 3:1 ratio of height to width. It all depends upon the function and the effect you are trying to achieve. The best advice I can offer is to draw the profile on paper and look at if/tweak it until you are satisfied. Then find a piece of wood that works with your design and give it a spin.
Platters and very shallow bowls are often the only way to showcase unusual figure, such as feathering in a crotchwood blank. The above rules don't apply for this type of work, of course.
Don't feel limited to simple segments of a circle for the wall profile. Consider ogee forms (e.g., s-curve) where the wall profile starts out at the foot as a convex curve, then has a transition into a concave curve. Try to put the inflection point 3/5 of the way up the wall. Or catenary curves, where the wall profile resembles that of a hanging chain - confusing, but look it up on the net and you'll see what I mean.
I like to use the profile to draw the eye to a feature of the bowl, such as especially nice figure in the wood, a band of inlay, or a turned bead or cove. But whatever the profile, strive for either a gradual change or a pronounced change in curvature . No flats or bumps, please.
Beads or coves look best when they come in groups of three.
I think bowl feet look best when their height is sized so that the bottom curve of the bowl is tangent to or very slightly above the surface of the table. Certainly not under the surface (a.k.a. cow flop bowls 🙂)! Goblet form can work too, if you want to elevate a bowl off the table.
Take the time to balance the grain. Unbalanced grain in a bowl looks amateurish, and can cause the bowl to warp asymmetrically over time. With a purchased blank, its hit or miss as to whether you can do this, but it's always worth trying. If you are so inclined, cutting your own blanks from a felled tree is a great way to solve this problem. Turning greenwood is fun!
Width-wise, I like the smallest diameter foot that keeps the bowl from falling onto its side . Functional bowls need a wider foot that do purely decorative bowls, but I try to keep these at no more than 25% of the widest diameter of the bowl.
Interior profile is best to be rounded. It doesn't have to be a perfect segment of circle, though if your exterior profile allows it that is a good target to try and hit.
Consider how the bowl will feel when picked up - a heavy bottom or a heavy rim will feel awkward, as will an excessively thin or thick band on the side.
Always try to make the best, not the biggest bowl! It's just wood, after all.