Arduino Capacitor Selection

I'm putting together my own board based on the Arduino Mega 2560. However, I've come to realize that I don't know much about capacitor selection (or non-theoretical capacitors, in general).
Are the non-polarized caps on the official Arduinos ceramic?
What voltage rating range should I be looking at?
Is there anything else I should know?

Thanks!

Yes they are ceramic.
As for voltage anything above the voltage that you are working at is normally fine but to be extra specially sure make sure you only run them at 80% of the rated voltage.
Selection depends on what they are going to be used for. On an arduino it is decoupling so ceramic is the best.

I assume these are "bypass" capacitors (between the power supply and ground)? You can use ceramic or monolithic . Really, anything will work*. And, a higher (uF) value won't hurt anything.

The voltage rating on a capacitor simply it's maximum rating** (if you put more than the rated voltage across it, you might fry it). You're probably not going to find any ceramic or monolithic capacitors rated for less than 25V, so that shouldn't be an issue either. It's "good practice" to allow some safety margin... If you have 25 Volts, you should use a capacitor rated for a bit more than 25V.

The only downsides to using a higher value or higher voltage capacitor is physical size and cost. In some applications the capacitor value is more critical, but in most applications a higher value won't hurt. And a higher voltage rating never hurts.

*Electrolytic and Tantalum capacitors shouldn't be used as bypass capacitors unless you put a ceramic/monolithic in parallel, because these capacitors don't always "act like capacitors" at very-high frequencies. Other types of capacitors (such as film capacitors) would work fine as bypass capacitors, but they are more expensive so they are generally used where the value and tolerance are more critical.

**The voltage rating on a capacitor (or transistor, etc.) is like the maximum weight rating on a ladder. As long as the ladder is rated for your weight or more, it's safe for you to climb the ladder!

100nF/0.1uF ceramic caps, 16V/25V/50V are all fine, I go with what's least expensive, such as

0805 not too small for easy handling.

X7R type capacitors will work. (C0G NPO works too, but expensive for such bypass duties... but if you have overstock of them, use it.)
You need a 0.1uf (a must).

If you also want to parallel a bigger cap, you can use a 10uf - 47uf too... but the 0.1uf is a must have.

Ideally use a 0.1uF cap on each supply lead (including AVcc) and really close to the relevant pin and use a ground-plane (or the best
approximation to a plane you can get).

Electrolytic - Big values (usually 0.1uF and up to multiple F) in a relatively small space, but horrible at everything else. Typically 5-20% tolerance. Used for anything where large values trump all else, like rectified AC-to-DC PSUs to remove AC ripple, or to store a reserve of power to negate the effects of sudden current draw, PCB inductance, minor continuity issues, etc. They're polarized unless you get bipolar, which is just two polarized stuck back-to-back. Voltages usually range from 5v to 100v. Typical through-hole form factor is radial: a can with legs on the bottom, or screw terminals for really big ones. Electrolytics can be "slow" due to ESL -- equivalent series inductance -- inherent to the package, so a low-value ceramic is often used locally to shunt HF noise. They also "age" more than other types, and will dry out and lose capacitance over time -- especially if they're not frequently used. Cheap as dirt.

Ceramic - Medium values (pF to a few uF) in tolerances of 5-20%, used most often to couple PSU noise to ground due to good ESR/ESL performance. Using a 0.1uF (100nF) ceramic in parallel with a 10-100uF electroyltic is an easy way to keep a nice steady reserve of noise-free power at the Vcc pin of an IC. Small values (10s of pF) are also commonly used for quartz crystal load caps, and RF filters at analog or power inputs. Ceramics are not polarized, and typically come in voltages of 25v to 250v or more. Can be either axial (lead at each end) or radial in through-hole form, usually radial with blue or tan colored disc-like head. Large ones used for AC PSU RF filtering and switch arc prevention are larger, have special safety ratings to fail open, and come in yellow, tan, or black. Cheap for reasonable values.

Film - Small values (pF to nF) with excellent tolerance (up to 0.1%, but normally 1% to 10%) used when performance is crucial. Often used for audio and video circuits, for filters (low/high/bandpass), and the like. Very good ESL/ESR figures. Not polarized. Physically, film caps are extremely large for their values. Typical through-hole forms are either radial blobs in a tan, reddish, or brownish color, or radial rectangular boxes of various shapes and sizes. Relatively pricey, and some niche caps can get ridiculously expensive.

Tantalum - Similar to ceramic, AFAIK. I don't actually know much about tantalum caps, since I've never used them myself (to my knowledge). I think they're polarized, but maybe not always. Someone will need to correct me if I'm wrong there.

Thanks for the help everyone. Lots of useful info here!

SirNickity:
Tantalum - Similar to ceramic, AFAIK.

Tantalum is nothing like a ceramic. Tantalum is an electrolytic and if the cathode used is MnO2 (which was the most common for a long time), it will have a very high ESR but a relatively low ESL. If the cathode is Polymer (which is newer) the ESR is going to very low. Polymer-based caps are acceptable for mid-to-high frequency bulk decoupling. And by bulk it would be 100s of µF at low voltage, something ceramic isn't good at achieving.

Ah, thanks James. I appreciate the correction.