What are the characteristics that a good portable piano should have? Considering that I will take frequent flights with it, what's the best I still can get for learning to play the piano?
Let's first look at what you need to have to learn to play piano:
- 88 fully weighted velocity sensitive keys
- A decent piano sound
- Headphones and a headphone jack (or speakers but they are not nearly as portable)
- A damper pedal and damper pedal jack
- Some place to put the (digital) piano
- Some place to sit
Those last two are actually quite important. Real pianos have a (mostly) fixed height above the ground for their keybeds, so putting a keyboard on random desks or whatever you have available will not really train your body properly for the real thing. Also posture and ergonomics are very important. So you need to be able to put the keyboard the right height off the ground, you need to be able to put your feet and the damper pedal under it, and you need to be able to sit at the right height yourself. That's all to say you need to get a portable folding keyboard stand and a portable folding piano bench.
To transport the keyboard itself, you should get an ATA hard shell case. They usually come in two different flavors: molded plastic or wood and steel or aluminum. While the wood and steel construction is trusted by many to be the most durable, molded plastic ATA cases are very resilient, cheaper, and lighter (in general). You may wonder about "TSA Approved Locks". The Travel stack has some info about that, including this question.
Headphones should be no problem. You can use normal headphones or high quality headphones or whatever you like. You may or may not need an adapter (1/4" to 3.5 mm).
The damper pedal may or may not come with the keyboard you buy. If it doesn't, buying a separate damper pedal is easy. They are fairly small and hopefully can fit somewhere in the keyboard case but if not can be put in regular luggage. Note that you may get more inspections with a damper pedal in luggage since it's an unusual looking bunch of metal and plastic on x-rays. You could also transport the pedal along with the stands.
For the keyboard stand, I suggest a table-style stand. Some are available that can fold up to a fairly small size. For the stool, there are folding stools that use X shaped legs and a padded seat that can also fold up to a fairly small size. But you don't want to check loose stands. I suggest either buying a separate piece of luggage to fit the stands or even a smaller ATA keyboard case (for a 61-key keyboard perhaps) or other kind of musical instrument case for them.
You should find a good music retailer who can help you with exact product selection, if you go this route. If you're shopping in the US, I expect you can put this together for $1500 - $2000. Also, you'll almost certainly be paying extra baggage fees. Before you even start to buy anything you might check with airlines about any baggage restrictions and fees they might have. And I suggest you figure out what kind of coverage you have or can get on your homeowners or renters insurance for these items.
At this point you might be wondering what the pros do. They do a combination of things, depending on the situation and the money available. First off, many tours use busses and trucks to transport people and gear, since flying is very expensive. When flying, instruments like guitars, basses, orchestral instruments (even basses and bassoons) are put in ATA cases, sometimes inside hard cases which then go inside ATA cases, and they are checked or in certain situations a seat may be bought for them or something like that. Smaller instruments will be carried on, usually.
For larger items (amplifiers, speaker cabinets, large keyboard instruments), they may be shipped in cargo planes if they are rare, vintage, personalized, etc., or a similar or same item may be rented at the destination. The latter is called "backline rental" and is very common for smaller tours by lower-budget acts. Some acts rent pretty much everything.
One final idea for you to consider is to search around the places you will visit for rehearsal studios or practice spaces. Some will have pianos or keyboards you can play. I practiced this morning at a place that charges $27 per hour with a fully weighted 88 key keyboard. If you find out that baggage fees for a setup like what I've suggested are high enough, it may be cheaper to rent at your destination and/or find rehearsal spaces you can go to.