My idea of a perfect cryptocurrency, in order of importance is:
1 - Secure from hacking etc (obviously)
2 - Privacy by default.
3 - Transaction fees should be a percentage
4 - Inflation - I think there should be either a hard cap of the total amount of coins.
5 - I think the idea of proof of stake is better than proof of work
6 - Current market cap, I dont want anything too small and obscure.
7 - Good GUI's, apps etc for peer to peer transfers etc.
8 - I am concerned about transaction speeds, [..] sub 30 second transactions [..]
Take a look at Ardor (ardorplatform.org). It is still alpha (testnet only) but is perhaps the only one that can fulfill your requirements - with the exception of point 3 (it has variable transaction fees) and 8 (~1 minute confirmation time), and it has an a little bit weaker privacy mechanism than Monero, but with Coin Shuffling you should be OK. It is proof of stake and secure (it doesn't need checkpoints like Peercoin-based currencies).
Its predecessor, NXT, has almost the same features, but will soon be outdated when Ardor releases.
A comment to your requirements 3 and 8: Fix "percentage" transaction fees will lead to spam if the currency grows and to scalability problems. Very low confirmation times lead to worse security. For example, a coin with a 30 second block time won't have even the same security with 20 confirmations than one single 10 minute confirmation in coins like Bitcoin, because the risk of orphan blocks is much higher.