The answer lies within your ears. No matter how many people type the explanations, it really boils down to listening experience.
I once was like you a few years ago and I had all these questions. Audio is a mystery in many ways and to really solve them, you have to spend the money and live with the gear to fully understand. Words of explanation can really do no justice.
Buy the budget amps and buy some expensive amps and live them for a while. You will get to know their sonic personalities. If you think that a cheap amp sounds great and the more expensive stuff is over hyped, you turn out be a great money saver.
However, if you end up loving the expensive amps, it could be a strike in the painful heart of your wallet.
I will say this from my experience on Head-fi:
Do not fully rely on people's opinions. Your ears and experience are most important. It is easy to say this but doing it can be difficult because in order to find the truth, you will probably have to spend money to have access to this stuff because you really need to live with gear to fully understand what they can do.