[jacquesm]

There are lots of controllers with weighted keys these days and plenty of entry level MIDI keyboards have excellent keyboards.

The big advantage is that you don't need to tune them twice per year and that extra budget is either savings or you can spend it on more lessons. A physical piano is nice (and even those can have 'MIDI out' if you look around for a bit or are prepared to do some DIY) but really not a must. I have both here and spend much more time on my digital just because it is far more convenient, I can practice on it at any time of day even when the kids are sleeping and the feel of the keyboard is as good as the real thing (Yamaha P515, not the cheapest but very good quality).