Pirakaphile,
It's ok! We're all in different steps along our audio journey
As far as all the cables, they usually include needed ones.
Portable amps usually include batteries, desktops usually need to be plugged into the wall. ClieOS has here reviewed portable ones.
Amp benefitssss... Controversial? But one thing people can agree on, larger headphones with less sensitivity than earbuds (or more ohms resistance) can sound "loud enough," but they need more power to sound controlled and clear at normal listening volumes. The resolution and detailed texture that you would hear with a nice amp will be a clear benefit... Maybe not "2x as good!" but once you get used to it everything else sounds like crap. How much you "need" to spend is the controversial part, it's really up to you.
Lastly, other hardware... Technically, no, but optionally yes. Say you have an iPhone 4S as your source, and a pair of Beyerdynamic DT880 (32 Ohms version). You'll be able to plug them straight into your phone, and they will sound more than decent, better than the earpods that came with the phone. However, plug something like a FiiO E11 into the phone's headphone jack, then the DT880 into the FiiO amp, you'll notice that you can distinctly hear the bass guitar separately from the lead or rhythm guitar, soundstage will seem to expand so you'll have a better sense of how far away from the mic things are or the room the performance was recorded in, and if you use a $11 line-out adapter (like a FiiO L11) you'll hear slightly better clarity (but you need an amp at that point to control volume anyway)... Basically, when people make the next step you are considering, they almost always say "I'm hearing things in my favourite music that I've never noticed before!" and "I'm rediscovering my music collection!"
Of course, a 600 or maybe even 250 ohm Beyer DT880 might not get loud enough driven off an iPhone...
If you get addicted, you can always spend more money. So, the saying around here for new people is
WELCOME TO HEAD-Fi! Sorry about your wallet.