Sundance_k1d got it pretty much covered.
Pianoteq runs reasonably well on my Mac mini at home, and it would run equally well on a "decent" laptop. It can be made to run even better on a respectable desktop, but there's nothing wrong with most modern laptops.
As far as the physical keyboard, there are hundreds of discussions on dozens of sites that deal with "what piano should I buy?". The piano subreddit has this question asked several times every week. The bottom line is this: Decide your budget, then if at all possible, and as much as possible, go to a music store and play on everything you can. If it feels cheap, it probably is. It won't feel like a "real" piano until you start spending around $2000 and up, although the Yamaha Arius line is getting pretty decent, starting around $900. Casio isn't anything to scoff at, either.
It sounds like you're in Hawai'i, so it's probably difficult to sample a wide selection, but if you're not picky, stick with Yamaha, Korg, Casio, or any brand you've heard of, and you'll probably be happy.
As far as the specifics of the connections.
Most "digital pianos" (console pianos) these days have a USB port. Plug that into your computer and it will see a MIDI device. Simple as that. I'm sure the "keyboards" (ie. synthesizers, stage pianos, etc) probably have this as well.
For speakers - If you're on a laptop, you can use headphones and the built-in sound of your laptop, or some desktop speakers. Eventually, you'll want to get a separate USB or Firewire sound device, but it's not necessary at first. If you're on a desktop, you can also use your existing sound, including normal desktop speakers.
To get fancy with studio monitor speakers, you can start out with something like the Alesis M1Active 320 USB. They are probably around $90, they plug into your computer via USB, and they are fairly decent speakers for the price. The simplicity is what I like most. Eventually, you might want better monitors like the M-Audio Bx8a's and a separate powered subwoofer, but this is also not necessary starting out, and it gets considerably more expensive as you upgrade.
Those are the basics. There are a few other things that might come up, but this Pianoteq forum is great at helping people get setup and fix problems.
Last edited by JerryKnight (28-03-2012 16:42)