Axis questions come up constantly, and there are three of them. Each one is answered by what the mark encodes, and a vague wish to be fair won't settle any of them.
You need the zero baseline where length encodes the value, and nowhere else. A bar's meaning is its length, so cutting the axis cuts the meaning. A line's meaning is the position of its points and the slope between them, so a line chart of a bond yield running 6.8% to 7.4% does not need to start at zero and would be unreadable if it did. A dot plot is a position encoding and follows the line rule. An area chart is a length encoding again, because the fill has magnitude, so it goes back to needing zero. State the rule as a question about the mark and it stops being something to memorise.
When should you use a log scale?
Log scales are for messages about rates. On a logarithmic vertical axis, equal vertical distances are equal percentage changes, so a constant growth rate is a straight line and an acceleration is a curve upward. Take a series doubling every year from 4.0 to 64.0 and then rising to 96.0 in the final year. On a linear axis the last step of 32.0 ties the largest rise on the chart, the 32.0 that came immediately before it, so the picture says the series is still climbing at full speed. On a log axis it is the smallest step, which is the truth: growth fell from 100% a year to 50%. Use a log axis when the message is about the rate of change, when a series spans more than about two orders of magnitude, or when several series of different sizes need to be compared on growth. Label it as logarithmic, because a reader who misses that will read the chart backwards.
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What about axis breaks and shared scales?
Axis breaks are permitted rarely and must be declared. A single extreme value that would otherwise compress everything else is the legitimate case, and the break must be visibly marked so no reader mistakes the gap for a real distance. The illegitimate use, and by far the commoner one, is a break inserted to make a small difference look big. That's the truncated baseline in disguise. If a break is doing the work of an argument, the argument needs a different chart.
One more axis decision belongs here because it is invisible. A shared scale across panels is what makes small multiples comparable, and auto-scaling each panel destroys it. Four regional sales series spanning 5.8 to 19.4 crore make the point: if each panel scales to its own data, one region's 0.40 crore fall occupies the same vertical distance as another's 6.60 crore rise, a 16.5-fold distortion, and the grid stops being a comparison and becomes a set of unrelated pictures. Layout comes later, but the shared scale is a chart-choice decision, so it's settled here.