1. By "Rack" I meant a rack case full of synthesizer modules, samplers. FX and all that gear. Don't worry - you'll have a few of those in the future!

2. Using your computer as a sequencer is easy.
You'll need a midi interface of coarse. They cost anyware between 100 and 2000 bucks.
And some keyboards (very few) connect directly to your computer via USB port.

For a software I'd recommend "Cubase" or "Cakewalk"(I think) if you're a PC user and "Logic" if you are a Mac user (which you should be if you want to do music).
But.... I suspect that you have a PC (windows platform), so I strongly recommend "Cubase". It's very easy to use, and whatever you don't know - you'll learn pretty fast.

3. By arranger they meant built-in (and sometimes programmable) rhythm styles. You know, "bossa nova", "Mambo", "Rock", "Polka", "Funk" etc. they are pretty good for birthday parties, funerals and stuff like that.
That's more of a PSR thing - professional keyboards and synths are normally used with the sequencer. Put it that way, If you want to be in a band - no PSRs! (unless you want to be in a Polka band.....(just kidding)

4. I still think that you should grab a friend and go check out some music stores. Talk to a few sales guys, ask questions about synths. That's how I learned. And ask a lot of questions about everything that comes to mind. People in the music stores (especially in the keyboard department LOVE to talk about synths, sequencers, samplers, vintage synths and all that.
And don't worry about sampling yet. First get good with the sequencer and Midi. Samplers are getting cheaper and cheaper - you may want to pick one up later.
As for other synth models....stick to big companies like Yamaha, Korg and Roland.
Support and reliability is the name of the game.

If you have any quwstions, please let me know.
Ed.