Ah, the age old question. I will elaborate.
Learning to play piano on a musical keyboard has significant drawbacks.
1) The full name for the piano is “pianoforte.” In Italian, this means, literally, “soft loud.” The precursor instrument to the piano was the harpsichord. On a harpsichord, no matter how hard or lightly the player depressed the keys, the volume that emerged from the instrument was unchanged. This was not ideal. To get around this there were double-keyboard harpsichords invented — play one keyboard and one string was plucked, play the second keyboard and two strings were plucked, resulting in a louder sound. The piano was an amazing invention because one could control the volume of the keys played by the pressure exerted by the fingers when playing — hence, it was called a “soft loud.” Most muscal keyboards do not increase/decrease volume according to the pressure used on the keys. This means that the student cannot learn one of the key components of piano playing with a musical keyboard. This is a large drawback which can be partially overcome by using a keyboard with “touch sensitivity” or “touch response” (or one of several other monikers.) However, the feel in the hand of such keyboards and the way it responds is markedly different than how it works on a piano, and does not translate well.
2) The tactile sensation of playing a keyboard is more similar to the tactile sensation of playing an organ, rather than that of playing a piano. Going between the two is something that has to be learned, and adjusted for. This is just one more thing for the beginning piano student to need to learn, and I don’t recommend it.
3) Most keyboards do not have pedals. Pianos generally have at least two pedals, and the damper pedal is used frequently — it is often introduced in the first level of piano playing. There are “keyboard damper pedals” and many keyboards have an input for these pedals. The less costly of these pedals work in the opposite way that an actual piano damper works — which is not helpful for a beginning piano student. It is possible (for most keyboards with inputs for damper pedals) to purchase a damper pedal unit that looks like and mimics the damper pedal of an actual piano — I do recommend this for use with either a keyboard or digital piano.
Acoustic pianos are beautiful and (can) sound wonderful –they can be purchased new or used. However, they are not good for people who need the piano on anything other than a first level of a building, who have stairs that a piano would need to be moved up or down, who live in small homes, who move frequently, or who need the piano practicing to not be heard throughout the house, clashing with other household activities. Figure in about $100/year to tune an acoustic piano. Do not get an acoustic piano from someone other than a dealer (or someone that knows pianos and that you can trust) without have a qualified tuner check it out first — old pianos that have not been maintained are sometimes wonderful and just need a little tuning — but sometimes they need a lot of expensive work and are not worth it. Most piano tuners do simple repairs and will be be able to advise you whether or not a used piano is a worthwhile purchase.
Digital pianos are an excellent option when an acoustic piano is not ideal. On the low end, the starting price is lower than the cost of a well-working acoustic piano. They are portable, can be used with headphones, and never need tuning. Digital pianos do a good job of mimicking the tactile sensation of playing a real piano, and it is possible to move with ease between a digital piano and acoustic piano. (There is still some variability — but for that matter, there is variability between different types of acoustic pianos.) Digital pianos often come with various “bells and whistles”: metronome, different voices, rhythms, ability to play midi files, ability to “record” (to midi) what is played and later manipulate it, and much, much more.
Ultimately, I recommend getting any beginning piano student an actual piano to play on — either acoustic or digital. Musical keyboards have a place — and for a parent that is wondering whether or not a child is “serious” about learning to play piano, an inexpensive musical keyboard can be a good way to get the student started, to see if the desire to play piano is a passing fancy, or a desire that will see the student through the effort required to learn to play piano. If a piano student continues beyond the first month or two — get a real piano.