So from Bitcoin's SHA256, there are many algorithm out there so far.
What is those's brief overview features, pros, cons?
What is best algorithm and why?
In general you can use
any cryptographic hash function as part of your PoW scheme. "Cryptographic" being the important part, as there are also hash functions that are not cryptographically secure.
So what's being used? Let's take a look at our top 10 PoW mineable coins according to Coinmarketcap:
1) Bitcoin -- SHA-256, obviously
2) Ethereum -- Ethash (note: Is planning to switch to PoS)
3) Bitcoin Cash -- SHA-256
4) Litecoin -- Scrypt (note: Is already overtaken by ASICs)
5) Monero -- CryptoNight
6) Ethereum Classic -- Ethash
7) Bitcoin Gold -- Equihash
8) Zcash -- Equihash
9) Verge -- Multiple hashing algorithms: Scrypt, X17, Lyra2rev2, myr-groestl and blake2s
10) ByteCoin -- CryptoNight
Most alt coins try to select PoW schemes that would be hard to implement as an ASIC. In especially ambitious cases they try to select algorithms that make it hard for GPUs to gain an edge over CPUs as well. In many cases this is achieved by requiring a lot of working memory / RAM, which especially for ASICs represent a challenge. Given enough financial incentive though, even those PoW schemes sometimes get broken (eg. Scrypt).
So it's not really a question of pros and cons, but rather a question of how ASIC resistant the PoW scheme really is, which is hard to gauge without in-depth research of each particular hashing algorithm. If you feel particularly fancy you could even look for hashing algorithms that are likely to be quantum-proof, albeit that might be still be a bit too premature to evaluate for sure.
Note there's also a case for ASIC mining making a cryptocurrency more secure due to the requirement of dedicated hardware. However that's a different debate.
Thanks for the lulz :D