If you want to compare acoustic piano and digital ones, they are more or less the instrument, digital piano are just cheaper, lighter and more quiet substitute. If you want to be as close as possible to the feel of a real piano, you'll have to chose wisely and to still invest a good amount of money. The additional features (organ sounds and stuff) are mostly gadgets in that regard. If you can afford the cost, the weight and the sonic disturbance of the real one, there's not much of a discussion here.
You will hear everything and it's opposite concerning digital pianos : some people claiming to having played acoustic pianos their whole life would say this one is really good while other, of the same background, would say it is a complete steal and would not lay eyes on anything costing less than 2000 dollars.
I would say you're good in the 900$-1300$ range, and you surely can have a bargain buying second hand. Yamaha is a good pick, but roland too, in my personnal experience.
If you know how to play a few chords, the best solution is still to go to a shop and make your own opinion. Digital piano might be as far to real piano as purists claim, but for now the only thing that matters is that it suits you. You'll have all the occasion to be picky in few years, when you're a more experienced player.