I'm looking to buy a capacitor variety kit to have on hand for various projects instead of buying individually every time I need one.
What's a good spread or what are the most common values used?
My projects range from single 3mm LEDs to the most demanding thing is a 256ct display of WS2812 LEDs.
I may have to make breadboard versions of breakout boards for a MSGEQ7 chip.
Is micro range fine? Do nanos or picos get used much for Arduino projects?
Do nanos or picos get used much for Arduino projects?
Yes.
100nF ceramic is the most popular capacitor value, although you can use a 0.1uF at a push 
That range is also useful when designing filters.
The 22pF is used to load the crystal for stand alone devices.
Basically it depends on the project. What I would do is that every time you want a specific capacitor value buy at least 10 of them.
Grumpy_Mike:
100nF ceramic is the most popular capacitor value, although you can use a 0.1uF at a push
Better change that name to Cheeky_Mike
But I might as well ask now- 100nf ceramic or 0.1uF electrolytic?
Ceramic 100nF are OK for decoupling logic, but not for analog/audio filters as they aren't linear and are
microphonic.
For analog electronics a wide range of plastic film capacitors is useful, 470pF -> 4.7uF, plus some largish
electrolytics for coupling/decoupling (10uF -> 470uF perhaps). For RF circuitry (less likely) small value
ceramics are everything).
But is analog electronics relevant?
I would buy a hundred or more of 0.1uF ceramic. Then about 10 of each of 10 values assorted from 10pF to 1uF. That range is useful for debouncing switches, balancing transmission lines and general experimentation. They should be rated for 25V or 50V.
Larger electrolytics are also useful. They get big and expensive in the larger sizes with larger voltage ratings, so you tend to pick voltage ranges closer to the system voltage. A handful of 100uF in 16V or 25 V is useful for smoothing power supplies up to 12V max. Get an assortment of bigger ones up to 1000uF if you are setting up a big laboratory.
You will need up to 10,000uF or maybe even more if you are building power supplies. Buy those individually when required.
But I might as well ask now- 100nf ceramic or 0.1uF electrolytic?
You struggle to find electrolytic capacitors lower than 1uF. Ceramics are a must for decoupling, one person used mylar ones instead and it gave trouble, here is the link to his question and solution.
http://forum.arduino.cc/index.php?topic=343563.10
I'd buy a kit of electrolytics 1 - 1000uF
and a load of ceramics 10pF - 220nF
should cover most requirements - and they're cheap on eBay etc.
regards
Allan.