A few comments - first some minor criticisms/omissions.
The calculated inductor value is a minimum, and so should always be rounded up to the nearest preferred value.
Similarly the max freq of this chip is specced at 100KHz, so the timing cap should be rounded up, not down.
When measuring the output ripple of a DC/DC on a scope, you should NOT use the clip-on ground wires on the scope probes, as the inductance of these is significant enough to make the output look a lot noisier than it really is. Most of the short spikes you saw on the scope were likely due to this. Instead you should use a very short (<1cm) wire from the circuit groundplane to the outer ring on the tip of the probe.
Also it is very important to have good grounding - a groundplane on at least one side of the PCB is highly desirable to get the best performance, increasingly so as frequency increases. It is quite likely that if you just plug it into a breadboard all sorts of odd things will happen. Most DC/DC datasheets have advice on PCB layout.
Breadboards can also have significant contact resistance, which can be a major issue with the peak currents involved in even failry low-end DC/DCs - when prototyping you really need to solder everything, and do not put the chip in a socket.
Input, and especially output capacitors must be low-ESR (effective series resistance) types, whch have the required high-frequency performance. If you're picking parts from your junk box, make sure the ones you use have 105 degree temp ratings printed on them, as these are generally also low-ESR - not always, but much more likely.
Now for some shortcut tips & rules of thumb if you can't be arsed with calculations...
In most good datasheets there are some example circuits with values shown.
Chances are one of these will be reasonably close to what you want - say within 50%, so use this as a starting point, build it and tweak as necessary.
Unless you have to really highly optimise for size or efficiency, leave the frequency as whatever the example shows
Inductor selection - the actual inductance is generally not at all critical. The current rating is usually a more important parameter. There will be a minimum value to avoid saturation, which will be inversely proportional to frequency, however a higher value will always work. Higher values also reduce output ripple in step-down configurations.
However you need to remember that for a given physical size, higher inductance values will have a higher resistance.
In practice 47-100uH will work with pretty much any run-of-the mill converter, and if you're not too bothered about maximum efficiency or minimum size, just use that, a least as a starting point. If necessary reduce the inductance until you see efficiency or dropout current fall significantly, then pick a value at least 25% higher to cover tolerances etc.
Similarly output capacitor values - due to the rather poor tolerance on electrolytics, you want to be generous in rounding up to preferred values - a factor of 2-4x is not unreasonable.
In most case you are interested in efficiency at a particular output current, so you can very quickly experiment with different inductors, diodes, frequency etc. by simply substituting parts and observing changes the input current - you don;t really need to go through plots at different load currents and input voltages unless you really need to optimise over a wide range.
Be careful when tweaking output dividers, as a momentary disconnection (e.g. in a resistor box switch) , partcularly in step-up configurations can cause destructive high voltages to be generated. The safest way is to fix the upper resistor (output to feedback pin) and tweak the lower one (feedback pin to ground) - that way any open circuit will make the output fall, not rise.