To really understand cryptocurrencies, you must understand Bitcoin. Not just its inner workings but where it came from and how it became what it is today.
The rest of the cryptocurrencies are only hoping to gain Bitcoin's popularity (which Ethereum is getting close to) that it maintained for nearly a decade.
Back in the day the following links helped me understand bitcoin:
http://www.michaelnielsen.org/ddi/how-the-bitcoin-protocol-a...
http://www.imponderablethings.com/2013/07/how-bitcoin-works-...
Once you properly understand bitcoin you are ready to understand other cryptocurrencies pretty easily. If some design choices don't make sense (secp256k1), then remember that Bitcoin's creation was close to when someone was caught doing something[1]. This is the answer to why many cryptocurrencies choose non-standard algorithms (aka. not NIST)