I teach with both acoustic and digital pianos. You don’t need a new piano, good condition second-hand is fine, but as with most things, you usually get what you pay for.
I suggest you have a piano where, all the notes work properly (no double striking, no sticking keys etc.), the piano should be tuned up to concert pitch (so you can play along with the videos and the CD). Pianos usually need tuning about once a year. Both these issues can usually be fixed by a piano tuner but it will be disappointing to buy a very cheap second-hand piano only to find that the problems with it are not fixable.
Although I have a strong personal preference for acoustic pianos, electric pianos will be fine for my lessons if they, have full size keys and weighted keys (made artificially stiff), are touch sensitive (goes loud and soft depending on pressure) and preferably have 7 octaves (though 5 octaves is sufficient initially)
Acoustic versus digital
I have a strong personal preference for acoustic pianos over digital ones. Three main reasons for this are expressiveness, value and the touch/feel of the keys.
It is hard to make a digital piano as expressive and responsive as an acoustic. The music on the Suzuki CDs is played on an acoustic piano so in order to be able to emulate the sound and expression as closely as possible it is best to have an acoustic piano.
Acoustic and digital pianos are often of a similar price for a similar quality, however acoustic pianos will hold their value far better. In ten years time a digital piano will have lost most of its value and if it breaks it can be difficult to fix. Once broken it is essentially worthless. An acoustic piano will be much the same in ten years time as it is today and its value is likely to hold well.
Touch and Feel
The ‘Touch’ or ‘Feel’ of the keys (how heavy they are to press etc) is also a consideration because it can be disheartening to think you are learning the “piano” only to find that you can’t play well on an acoustic piano because you are so used to the distinctive “keyboard” feel of instrument at home.
I suggest that you get the best quality instrument you can afford. As a thinking exercise imagine that you want to take up sewing as a hobby. Consider the difference in your enthusiasm level if you got a good condition sewing machine, capable of producing quality items, compared to if you got a poor-quality machine where the needle kept jamming or pulling holes in your fabric. Which would you be more likely to want to continue with?