1 - Secure from hacking etc (obviously)
That is largely a function of your capabilities and knowledge, not the project you invest in.
You have to set up a hardware wallet, and follow other best practices.
I am not saying there aren't differences of security with different ecosystems, I am just pointing out that primarily (largely) it is a function of your effort and capability.
2 - Privacy by default. I am mainly interested in coins such as Monero, Dash etc. I am new to cryptocurrencies and am of the impression that Monero is the most secure of the top 10 coins by market cap. I'm happy for you all to tell me otherwise.
In terms of security of the blockchain against 50% or 33% selfish-mining attacks, that would probably be Bitcoin.
4 - Inflation - I think there should be either a hard cap of the total amount of coins. Coins with very low pool inflation rates are acceptable to me, but, I would prefer the hard cap (another reason I dont think Monero is quite perfect for me)
Proof-of-work has a tragedy of commons failure without a perpetual block reward. Recent published white papers have proven this.
I will be making an altcoin that has a perpetually shrinking money supply (infinitely divisible so it never reaches zero). I can do that because mine won't be proof-of-work.
5 - I think the idea of proof of stake is better than proof of work for the purposes of just simply not wasting huge amounts of electricity for a currency. However, my current understanding is that there is no particularly secure proof of stake option currently, so, maybe thats something that would need to be implemented later. I guess the question from me here is could Monero (or whatever coin you are recommending to me) switch to a proof of stake later if a secure one came out?
Only proof-of-work can remain unstuck without whales. Only proof-of-work doesn't have nothing-at-stake and other problems of Byzantine agreement.
However, I am about to introduce a radical new consensus algorithm which doesn't waste electricity and doesn't have those problems.
6 - Current market cap, I dont want anything too small and obscure.
Stay away from mine then, as it is currently vaporware.
7 - Good GUI's, apps etc for peer to peer transfers etc. I believe this is another current Monero issue, though I do know they have a GUI wallet now.
Dash may have these, but the anonymity of Dash is a joke.
8 - I am concerned about transaction speeds, though my understanding is that more mining = faster transactions so its an issue that can be resolved later if it becomes a serious issue with higher transaction fees yes?
Incorrect. Transaction speed will only be improved with a radical new consensus algorithm. Dash's InstantX is seriously flawed. I found a high school level math probability error in its web page "white paper".
I am definitely after a coin that has the potential to go mainstream in shops etc, so im not interested in any coin that could not facilitate sub 30 second transactions by any method.
Then there is nothing you can invest in at this time. Well maybe Steem...but there are other issues with it...