I travel a good bit, but you don't have to get on airplanes to find great opportunities to create a quick piece of art.

I like to use watercolors when I'm able because:

1. They are easy to prep, because there really is no prep other than having some liquid available. Yes, I've been known to use coffee during business conferences if it would have been impolite to get up to get a glass of water.
2. They are inexpensive, relatively. Watercolor sets are WAY more affordable than acrylic or oil.
3. Unless you are trying to be photo-realistic, watercolors almost require a sense of playfulness that fits a beginner or amateur well. The media gives you a perfect excuse for not being precision-focused in your explorations.
4. There is almost no clean-up or mess.
5. A good set will last you years. The larger set in the featured photo above as been traveling with me for 15 years. I've had to replace a pan or two once in a while, but it's definitely been worth the investment for a semi-premium 24 color "half-pan" set.
6. The little 12-color set is super easy to take everywhere. I have several of these sets - one in my travel bag, one in my motorcycle pannier, etc.

Recommendations:

For your "Primary" set I recommend a 24 color half-pan set something like what I have in the photo above. I honestly can't find the exact product that I love so much - maybe they don't make them anymore, but look for these elements:

1. Replaceable/Refillable "Pans" - If you go through your favorite color quickly, or hate a color in the set and want to use a different one, these little modular plastic pans are wonderful. Mine can also be re-arranged to fit my personal preferences - like putting flesh-tones in one area.
2. Room for a few different-sized brushes.
3. Plenty of room in the lid or another palette element to create washes and blends. These kits are not designed to give you the volume you'll need for art bigger than about 10x15 inches. Think about the size of paper you can fit in your backpack and these will be fine. For images larger than that, you'll want to buy tubes of watercolor and use a larger pallet such as a dinner plate or ice cube tray.
4. I like the center area of my larger kit because I was able to add 4 more pans, plus room for some watercolor crayons. If needed, my tray could hold 36 half-pans of paint.

Super-Small Travel Set:

Winsor & Newton Cotman Watercolor Paint Set, Sketchers' Pocket Set, 12 Half Pan w/ Brush

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Primary Watercolor Travel Set: 24 Color half-pan set.

Windsor & Newton Professional Watercolor Paint Set, Lightweight Metal Box, 24 Half Pan

This isn't my exact travel kit, but it's comparable and will serve you well!

Examples of traveling watercolor work.