I have played and loved playing both a Nord Electro and a Korg SV-1, so I am no detractor of electronic keyboards. However, there is a significant difference, in my view, when playing an acoustic piano - or at least a certain sort of acoustic piano.
The sort I mean has two features: acceptable key and pedal action, and pleasing tone.
There are many new and even expensive pianos that have neither. There are pianos people are trying to give away on Craig's List today that have both. Much like finding the love of your life, it requires you to look and it requires you to be lucky.
The only sort of piano I would warn you away from is a spinet. The best of them I have ever played lack both my requirements. Anyone who has had a different experience, please chime in. There are exceptions to everything in the world, are there not?
But there is something about my old 1924 upright, purchased almost 30 years ago for $900. It is a structure made mostly of wood. When I sit down at it, I sense the living material that welcomes me onto the bench, and sonically, into its arms.
The subtleties of touch and tone that an acoustic piano offers, the range of expression, feels grander, and yet smaller - perhaps more subtly scalable from subtlety to grandeur. If I could carry the thing to every gig, I would not hesitate.
As user18834 indicates, the point of contact between the instrument and you is your fingers - though your foot on the pedals is important, too. But given the way the sound swims around you, it is much more of a whole body - perhaps a whole soul - experience.
So, seek out the best piano you can acquire given your means. And the best will feel the best - great touch, tone that moves you, from the lowest to the highest key on the board. Don't jump at the first one that might do - hold out for the right one. You will play it the rest of your life.